If you want to seriously use it, get MorphOS and learn some amiga shit. You coulsd install gentoo if you wanted, but the ATi 9660 in the eMac's is completely different than a normal 9660 in PC land. MorphOS will give you a snappy computer to get on the net with. Past that you will have to learn the amiga crowd.
OSX may be neat to run for a while, but if I remember that thing has a G4 7447-A2 at anywhere between 1 GHZ and 1.42. OSX was NEVER great on these things and I yearn for the day that its a flat price for morph.
If you're going to be using OSX you have 2 options:
1 - Use 10.4 and have classic as well (OS 9.2) as OSX available. You use TenfourFox/bird for browsing and email and have 9.2 stuff available to you as well, though with some back fire. At least you can play Deus Ex on it. Also with 10.4 you have at least SOME memory management in ram.
2 - 10.5. If I were you I wouldn't use OSX at all. Its a memory whore, even 10.5. You're lucky if thats one of the ones that went out in 2006 because at least it has a jump clock and PC2. In 10.5 you'll have the newest apps possible and the best utilization of the GPU possible. However unless you have some way to utilize memory management and a way to keep the god damn swap turned on, you're fucked in 10.5. At least you can play roller coaster tycoon 3 right?
And in linux you'll have a pain in the ass just getting anything to install stable. I can't get anything to run consistantly. 7 years ago when linux and ppc were on fire in the same whole maybe it would have been better, but unless you can do your own kernel and are willing to use Mesa and get 0 GPU performance you're fucked.
I hate to spin doom, but apple never really thought this shit through. They supported the M68k systems until 2004 for a reason. These machines never were utilized correctly and it seems the amiga crowd and some independant OS crowds got it right. Tie the GPU to the CPU and use the CPU for GPU overhead, and either absolutely populate the RAM and bus, or don't use it at all. People want to make Big endian procs play by little endian rules, then the system doesn't run fast, then they complain powerpc is slow and terrible. Well, it is, but only if you're retarded and don't look stuff up on the shit you don't know.
Problem with morph is it has a retarded license that no one understands. Problem with OSX is it was never actually made correctly for PPC. And the problem with linux is no one learns how to make a decent kernel in big endianess. Now, if you don't mind 75/80 bucks on a lisence, morph OS will make that emac about as fast as your desktop. I can bet on that 95% (depends on the clock rate really).
I recommend look up what PPC can do nowadays for what you want to do. Look at the speed of your hardware and stuff the thing with ram. Some machines you could put 3 GB ram in with a hack, most could only do 2. Honestly 2 GB is enough for it so don't be discouraged by that. Past that, you can message me about anything you need to know on OSX or Morph and I can help where I can.
Oh, and get the biggest fucking HDD you can find new. Just trust me on that. If you can get swap to work in OSX, if you go that route, make a BIG file. Like 12 gigs.
Good luck!
Edit: I made a G+ for ppc macs as well.
https://plus.google.com/communities/109971737503498795155