In no particular order:
I don't know about the G3 upgrade, but I guess it'll work, Amiga PPC cards are supported, and they're easily as much of a hack as putting a CPU in the cache slot
I have absolutely no clue about antialiasing in X
So, onto Distribution choices.
I"m a Debian freak, it's advantages, for me, are that it doesn't have the easy stuff masking me from the internals, and I can run it in a vastly stripped down config. so I'm probably not the best person to be giving advice.
Anyway, from your point of view, it has a huge quantity of binaries, the current PPC distro ships on 7 CDs, but the installation procedure is not for the faint hearted.
I'm not too keen on Mandrake, but it is easy to set up, I'd be surprised if it only worked with new world machines... The setup should be just as robust on PPC, there isn't that much different between the two once you've dealt with partitioning and boot setup, it's just another Linux system.
I'd suggest though, that you go with YDL, IIRC both that and Mandrake are RPM based, so packages should be compatible between the two. Part of the beauty of Linux is that regardless of which distribution you use, all software written for Linux will work with it, though in the likely event that a PPC binary isn't available you'll have to compile, it isn't that hard.
The best thing to do is to experiment with different distributions till you find one that suits, it does depend also on wether you want to run Linux or learn Unix, if it's the latter then you'll be better off with something more old-skool like Debian or slackware, whereas the former is better facilitated by Mandrake, and probably YDL (I haven't used it, but a friend swears by it for PPC, though he likes Slackware/Debian too...)
I hope this serves to clarify more than it confuses...
