1.8.9 (duh), 1.12.2 (last version with great VANILLA performance on many computers), 1.20.2 (version i primarily play on), Beta 1.7.3 (for pre Adventure Update experience)

i mean if solely for archiving i'd probably try to get my hands on every version

but going by what i'd actually use? probably 1.8.9, and 1.20.4 as those are the two that'd i'm currently using the most (1.8.9 for whenever i play hypixel and 1.20.4 because it's the latest version + a private server that i'm apart of uses it)

1.20.4, the more stuff the merrier

specifically 1.6.3 because it was the console edition

All of them

1.9 for sure.

I guess beta, it is a fun game with more hadrness

i usually keep 1.12.2 for compatibility, a few versions from about 1.5-1.8 for testing or whatever, but I also like beta 1.7.3 as it being the last update before the game became half of what we know it as today - it's a really unique experience. 1.15 is probably the last update before the games was changed so much to be almost unrecognizable in some aspects, so I support that version as well.

Assuming you don't just keep 'all' [By which I mean the last stable version of each major release]:

1.6 for the old caves
1.7.10 b/c of popularity with modding
1.12.2 (unless you want the old fractal update map chunk loaders in which case 1.12.0) as the last with the old water
1.13.2 last with the door based villages
1.15.2 last pre nether regions update (i don't think offhand of anything in 1.14 that 1.15 changed for ill )
1.16.5 last pre altitude changes
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beyond that I've not followed closely enough (if pushed I'd just skip 1.17 and keep 1.18.2 & 1.19.4)