You roll one die of the base damage for the crit damage. So if it's a 2d6 base damage, the crit die is 1d6. If it's a 1d12 base, the crit die is 1d12.
Yep. The GS averages better, but if you can get an 18-20 crit range (and a Fighter can), they're virtually indistinguishable, DPR-wise. Plus as noted, swing-y damage is an attraction in and of itself to many players! And the difference is just never that huge (0.35 DPR even at 20-only crit, assuming one attack).
So I think the GS/GA example is actually kind of okay, even decent.
However, I do think this is the least exciting weapon list I have ever seen in a modern edition of D&D (and actually, 1E and 2E also had way more exciting weapon lists). It's problem isn't so much the mechanical questionable-ness of some of the weapons (yes, it is me saying that, good lord!), it's more that they're really boring. Like whoa boring. They're same-y, and almost none of them have cool properties or tricks of things that make players enthusiastic about them.
You were dead right earlier when you said most players don't CharOp. What they do, in my experience, is peruse weapon tables looking for stuff that looks/sounds cool (both 3E and 4E had pretty weak illustrations for the weapons, hope they do better with 5E), or which does special things, and this list doesn't really offer that.
Personally, and I know many may recoil in horror from this, but I am beginning to miss 2E's "different damage on size L+ targets", which helped differentiate a lot of weapons (I wouldn't emulate it precisely, of course).
Also it is just really odd that a 1h Quarterstaff does 1d6 and a club does 1d4 and the club isn't even versatile, which just makes less than zero sense. Why is a club not versatile? I'm seriously trying to come up with an explanation here. Virtually all combat-clubs except those used by modern police can be easily gripped with two hands - it's an ICONIC image, the club raised in two hands.
The presence of the greatclub confuses matters even further - so we have, like, a club so small you cna only wield it 1h, and a club so big it can only be wielded 2h, but we don't have, like, a normal size club? Where's Goldilocks when you need her? Presumably being hit by a medium-sized bear armed with a medium-sized club or something...
Also quarterstaffs are versatile but don't have reach and aren't double-weapons? Huh? Seems like the quarterstaff stats are, in fact, the "medium club" stats, and that an actual quarterstaff should have different stats.
Bored and confused by this table.