I also heard WinME has a few problems, and not just a few.
Driver compatability can become an issue, the hideous restore feature and horrid use of virtual memory..
Me can be tweaked to work pretty well, but if youre new to computers, I'd take Win98SE with _all_ updates from the microsoft.com.
However if you think 98 is outdated, by all means try W2k pro. It's very stable if your system has over 128Mb ram (if you get 1.33 T-bird I'd expect you get at least 256..)
In game use, some older games wont work with w2k but generally speaking it's very good also for game use. Only problems may come if you have some special brand joysticks etc.
I have SB Live! (ok, the drivers suck at w2k still.. but it works.) And ms precision pro which worked without a glitch in w2k (ok, the sidewinder command central didnt install on w2k even that it says it should in ms page.. M$ rules!) Even though there are those small annoyances, it's working and thats that.