Well, I would think that the "best" OS for the task would depends on which games you're talking about; but that aside for the moment, OS X in general was... not very good until 10.3 or thereabouts, so I would start there.
While 10.2 was fine with using OS 9.1 in classic mode, 10,4 (Tiger) needs 9.2.2 to run classic good.
Classic is the name of the emulation environment, that lets OS 9 work under 10.4 (no reboot necessary), but if your Mac is still capable of Dual boot, you should use OS 9 directly for OS 9 games.
On an ibook G4 with 1,33GHz I get a stuttering mouse in Master of Orion (strategy game, not much action, just calculates where I move the mouse pointer).
Yes, one of my all time favourites. I stepped in, when it was Version II, I bought Version III for my brother (Windows) some time later, but we did not get very far with that.
Although, if you have played it several times, you know the ways how to get to the end and win and you find yourself from one point on doing the same steps again, I play it still one time in a year, partly for nostalgia reasons.
I still play a lot of games in 10.4.11. Games like Tron 2.0, Undying, MTX MotoTrax and VGP2 are still fun to play in my opinion. They work great in Tiger. A lot of the reason I keep PPC around is for the older games.
It was a minority of games that was released for the early OSX's, so I would definitely say 10.4. Even then, I would be surprised at how many games you could find that couldn't run on 10.6.8, so maybe look that up.