I don't know what information the game supplies (I got it for Christmas, but haven't yet had a chance to install it on my gaming computer) but you can look up the rules for the tabletop game on this site. I don't think there's a page directly comparing the "chasses" of each class (ie their BAB, saves, skill points, etc) but you can easily check things by looking at the entries for each class.

To address your actual question, the base attack bonuses ("base", incidentally, not "basic") of the classes follow three progressions, which are unofficially referred to as fast, medium and slow. Fast gives +1 every level, medium gives +1 in three out of every four levels, and slow gives +1 every other level. BAB is also almost invariably tied to hit dice (ie how many hp you get per level). Slow progression gives only 1d6 (meaning that when you level up you either roll a d6 and gain that many hp, or just gain the average of 3, depending on which rule the game is using; you also gain your constitution bonus in extra hp each level on top of that). Medium gives 1d8. Fast gives either 1d10 or 1d12, depending on the particular class.

Archetypes almost never change the chassis of the class, so (for example) the BAB progression of a vivisectionist is the same as that of a standard alchemist.

The classes' BAB progressions are as follows:
Alchemist: Medium
Barbarian: Fast
Bard: Medium
Cleric: Medium
Druid: Medium
Fighter: Fast
Inquisistor: Medium
Kineticist: Medium
Magus: Medium
Monk: Depends which version the game is using. The original monk had a medium progression, but a revised "unchained" version was later released which has fast progression. If you're unsure, I suggest comparing the unique class abilities of the game's monk to that of the standard monk and the unchained one, and seeing which they match up with.
Paladin: Fast
Ranger: Fast
Rogue: Medium
Sorcerer: Slow
Wizard: Slow

If I've forgotten a class in the game, check the SRD I linked for the information for that class.