Some games do require DOS 5 or higher but I don't recall ever seeing any that specifically required DOS 6.
I'd advise against using DOS 4 as it had some nasty bugs in it that could cause data corruption; it was pretty notorious in its day.
I'd suggest either sticking with 3.3, or if you need FAT partitions >32MB use DOS 5 or newer. (Compaq DOS 3.31 also supported these size partitions if you can track it down).
You may also want to give FreeDOS a try, I haven't run into any problems with that.
