You could have been forgiven, had you been in the Beastie Boys at the time, for feeling like your life had reached something of a crossroads in 1998. Not in the way that the phrase often implies, of an impending need to take a decision that will upend everything that had gone before and which would carry an implied risk. Rather, just before the turn of the century, the Beasties had put themselves in the enviable position being able to do pretty much anything they might have wanted.

The would-be hardcore band who discovered rap and inveigled their way into the music's mid-80s creative explosion, AdRock, MCA and Mike D had become superstars with music borne out of a kind of performance art satire that went over the heads of most of the huge global audience they attracted. Licking their wounds in the couple of years following Licensed To Ill's global success and the band's resultant infamy, they made an LP with a couple of DJs from Los Angeles, Paul's Boutique, which was hailed as a masterpiece even as it moved the decimal point to the left on the number of people who bought their records. Two further albums followed in the early 1990s, each a kind of retrenchment, with the trio going back to their guitar/bass/drums roots and ransacking their eclectic record collections for inspiration as they flung rock, punk, funk and rap at the walls of their self-built studio and found that pretty much everything stuck.

Along the way they'd renounced the worst implications of their earliest lyrical excesses and become, amid the still unconstrained (and unconstrainable) silliness that ran through everything they did like letters in a stick of rock, a progressive voice capable of speaking common sense and offering a very individual brand of affirmation and inspiration to an unusually broad constituency. They were elder statesmen of rap, and hip hop fans respected them because Paul's Boutique was a golden age touchstone; they had their own label and magazine and played their own instruments, so indie fans who usually ran a mile from rap could get with the programme; the Tibetan Freedom Concerts instigated by MCA gave them a position as pop's conscience that rivalled U2's, but without any of the supposed po-facedness. If you were in a band you wished you had a quarter of the freedom the Beasties had earned for themselves.

What they did with that freedom was make their best LP – a record rooted in rap but drawing on whatever they felt like playing, with no limits placed either on compositional approach or instrumentation. Other albums may help the listener recapture specific moments of their youth more efficiently, but Hello Nasty is the single best distillation of everything that made the Beastie Boys so great. It's got the humour and the punch of Licensed To Ill without having to lug around any of the uncomfortable baggage (bar one ill-considered ableist phrase on 'The Move'); it takes the sampledelic cut-and-paste ethos that fuelled Paul's Boutique but brings it all inside the Beastie tent (as great as Paul's is, it's a collaboration with the Dust Brothers, including some material that wasn't written with their voices or rhymes in mind), and finds a way to slot it in to the jam-band punk/funk approach that was let off the leash on Check Your Head and Ill Communication. It allied the trio to the best DJ they ever recorded with – Invisibl Skratch Picklz iconoclast Mix Master Mike – and as well as containing one of their biggest signature hits (the magnificent sci-fi brag 'Intergalactic') there's precious little across any of the four sides of vinyl that wouldn't have made an arresting single. The balance between traditional beats-and-rhymes hip hop and band-driven song-structure tracks tilts towards the former but feels that an equilibrium has been found that had perhaps eluded the band on the preceding two LPs. It is also beautifully recorded, the different sonic elements - be they the outrageous steel-band samples of 'Body Movin' or the echoey vocoder hooks of 'Intergalactic', the gargantuan sound of Mix Master Mike's needle excavating the grooves of his records during 'Three MC's And One DJ' or the spaciousness of the live instrumentation on 'I Don't Know' and the unabashedly ridiculous 'Dedication' – each slotting into their exact position with all the quality craftsmanship of one of carpentry whiz Keyboard Money Mark's dovetail joints.

Best of all, it's a record that revels in a creative freedom given greater impetus by the band's growing experience. Where Check Your Head inevitably holds a sense of ever-so-slightly hesitant experimentation - the three principal band members not yet certain that everything they tried was going to work – and Ill Communication, particularly since it came so relatively quickly afterwards (it was released two years and one month after Check Your Head, the shortest of any of the gaps between the band's eight studio albums), seems to be cut from very similar sonic cloth, Hello Nasty stands on its own. You can still hear the different constituent parts and you get a strong sense of where they've all come from – and often that's the same place that the same sorts of songs or ideas or styles came from before: but everything here has a homogeneity that means songs as absolutely different as, say, 'Just A Test' and 'Dedication' feel like they belong on the same LP. In the midst of this, the group get to perform a rare kind of studio alchemy: not only does the record fizz with the audible freedom its makers had worked so hard to win for themselves, but they manage to get some of that unbridled joy to show up on tape. There will be listeners for whom 'Dr. Lee, PhD' is self-indulgent nonsense, but if you can listen after gagging your inner cynic you'll hear something magical as the Beasties and friend/producer Mario Caldato Jr. sit back in awe while Lee "Scratch" Perry improvises a song over a track they'd made while under the influence of his back catalogue. And it is not just his untimely death that gives the MCA-sung and written 'I Don't Know' an affecting potency: it's one moment among several here that underline the fact that, no matter how confident and assured the group now felt with the unique way they'd found of making records, there were still new possibilities worth them trying to explore.

Rated by AdRock himself (writing in 2018's consistently fascinating and often very moving Beastie Boys Book) as his favourite Beasties album, Hello Nasty is receiving a slightly muted commercial fanfare to mark its 25th anniversary. The big effort was expended in 2009, belatedly saluting its 15th, when it was remastered and re-released as part of a wider Beasties catalogue rejuvenation programme. A four-LP version of Hello Nasty was released as a slipcased box set, in an edition supposedly limited to 1,500 copies. This was available from the band's website as late as 2018, though it isn't clear whether these were unsold copies of the original run or a subsequent repress. This year's model is, we are assured. A promised review copy had not arrived at the time of writing – a new repress of the 2009 package. It is also limited, though there is no indication of how many copies have been manufactured. Not enough, anyway: it's been sold out on the band's UK website for at least a month ahead of this weekend's release date.

The box includes the original record on two pieces of vinyl, and a second double-LP's worth of remixes, outtakes and associated aural ephemera. There's nothing here that will be new to long-term fans: the extra material was available in the original box set and on the two-CD version of the album also reissued in 2009. (The 25th anniversary product range includes 14 t-shirts, hoodies and sweatshirts, five of them in children's sizes, but no other formats containing the music – almost as if the LP at the heart of everything is the least important aspect.)

The extra tracks include some interesting and worth-hearing material, but suffer from some of the perennial problems that mean archival, box-set-type explorations of hip hop classics remain a good deal less exciting than comparable efforts from other genres. There aren't, usually, multiple takes of different songs, showing how the artist worked their way through the ideas until arriving at the version that got released (though the Beasties' method, at this stage of their career, means that there are at least a few of these, and – credit due – they're included here). If there were demos recorded before the album sessions started, even if they use the same samples as the finished versions, they'd count as new releases for sample-clearance purposes so a lengthy process of dealing with the original artists and/or their estates would have to be completed (and money paid out for the necessary licenses) before they could be included on new releases. For all that there might be a few thousand fans who'd gladly pay to get a clearer sense of how a favourite LP got made, it's unlikely there'd be enough of them to turn a profit. So where, say, Bob Dylan fans can, if they wish, listen to a whole CD of different versions of 'Like A Rolling Stone' (one of 18 discs in the fascinating and frequently flabbergasting The Cutting Edge box set), or Miles Davis fans can get to hear him and his quintet talking through how to play every track on the brilliant Miles Smiles (studio chat, false starts and alternate takes are all included, alongside the final versions, in the absorbing Freedom Jazz Dance four-CD box), the equivalent archival releases in the hip hop world generally have been limited to adding instrumentals, remixes and the occasional out-take – many of which had often been released as b-sides – to remastered versions of the original LPs.

To be fair, the additional stuff here does show that some effort to redress this balance was made. There are bits of studio chatter that shed some light on the atmosphere during the sessions, some false starts that are at least mildly diverting, and, because this is still the Beasties in post-Check Your Head mode, there's the occasional in-the-studio jam that didn't make it as far as becoming a finished song. In between them, half a dozen remixes (all released on singles taken from the album) give a backbone to the 55-minute track list. When this set was originally released, many reviewers felt the need to pile in on the Fatboy Slim remix of 'Body Movin', holding it up as an example of why big beat was a waste of time, the blend of melody and thump like adding a fat-tip moustache to a much-loved portrait. Unearthing it anew today is like stumbling on an intriguing time capsule, the remix sounding more resonant of the late 1990s than anything on the main Hello Nasty album, but it holds up as a fun take on what was an exuberantly silly song – the Beasties' belated entry into the dance craze subgenre – to start with. What remains disappointing is that this reissue finds no space for his remix of 'Intergalactic', nor those by Alan Braxe and Soulwax; nor Handsome Boy Modeling School's take on the conceptual delight 'The Negotiation Limerick File', or the live version of 'Three MC's And One DJ' that was recorded during the shoot for the video.

This box set may also prove mildly controversial, perhaps among owners of the original who might feel a new pressing breaks an implied promise to those first 1,500 buyers, but also for those fans who find the 2009 remaster somewhat problematic. The comparison available to this writer – 2009 CD with 1998 vinyl – suggests the remastering is pretty subtle: perhaps a light dusting-off of the original master tape, a little bit of enhanced separation in some of the more sonically dense portions, an ever-so-slightly widened soundstage, perhaps a touch more boom to some of the bass. Some of those who've heard the 2009 vinyl version complained of sibilance problems, particularly on the record's outstanding first side – though there are some who claim that side three, track one ('The Grasshopper Unit (Keep Movin)') of the original vinyl version has a pressing fault that renders it unplayable without careful adjustment of tracking weight and anti-skate settings. Whether these are widespread issues, defects in individual copies, or problems caused by a demanding record asking too much of a particular person's turntable, you'd hope that, as part of the time, trouble and cash invested in this latest re-press, someone might have taken the opportunity to correct them. But without a copy to listen to, it's impossible to say whether this has happened or not.

Ultimately, perhaps, none of this much matters. There is no substitute for listening to the best-available reproduction on the highest-fidelity system you have access to, but even if it's a low-bit-rate stream coming out of a tinny smartphone speaker, Hello Nasty is still more than worth an hour of your time.

Hello Nasty is re-released via UMR on September 8