Aside from OS4.0, which is the best all-around 3.x series? I've seen 3.0, 3.1, 3.5, and 3.9 come up a lot.
3.5 and 3.9 both come with 3.1, so either one is quite ok. You will need to update a basic A1200 a little to run 3.5 or 3.9 well (extra mem, hard drive and such), but 3.1 is ok with a basic system and is still reasonably well supported. Anything older than that isn't really useful with an A1200 anyway, since it has either 3.0 or 3.1 kickstart ROM's inside it (update to 3.1 if you happen to get an old model, the new OS's require it). There is really no reason to use 3.0.
There is of course the thing that 3.5 and 3.9 arrive on a CD, 3.1 was still floppy based. A CD drive will be quite useful though, for transferring stuff from a PC in the initial install phases (a lot of stuff can and need to be downloaded from the net). Naturally a hard drive is a practical must-have for anything else than nostalgic gaming.
For really old games it's better to get an A500, but that's a different discussion.