On my 520c with 12mb of RAM I have 8.1 (and virtual memory turned on), and on my 540c with 36mb RAM I have 7.6.1.
Yes, that order is a little odd but that's besides the point. Both OSes seem to run decently well for light gaming of the era (aside from the 520c's display being prone to ghosting with fast moving images).
If you only have the base 4MB of RAM stay with 7.1.
At 8mb you could comfortably use up to 7.5.5... 7.6.1 would be crammed a bit.
12mb of RAM is safe for 7.6.1. 8.1 can install and run but expect to need Virtual Memory turned on. Depending on what you use it for this may cause performance hits.
Like Byrd said, once you are in the 20s of MB of RAM you are plenty comfortable for 8.1 if you want to run it. 7.6.1 obviously is still a good choice as well.
8.1's two big draws (for me at least) are the updated Platinum UI and the ability to read/write HFS Plus disks. If you ever need to work with a CD, ZIP disk, or external drive that is formatted from OS 8.1 and above there is a chance that it may be HFS Plus (depending on what option was selected when said disk was formatted/burned).