The OP says that he is new to using computers and wants to play games. I'm going to go out on a limb and guess that the kid is about 12 or 13, in which case the computer was probably given to him. Like someone else said, if it wasn't given to you, I sure hope you didn't pay a lot of money for it.
Sure, a $300 emachines would be a much more cost effective upgrade. However, when you're 13 years old, $300 doesn't just fall out of trees, at least it didn't when I was that age, which wasn't too long ago. If a new computer is out of the question, there are a few cost effective upgrades you can do in a 'lint and buttons" price range.
First, you can probably upgrade that CPU to at least a 1.1 ghz Celeron chip if you use a slot1 adapter. You can probably find both on ebay together for $30. Heck, I would throw my PIII 550 Mhz chip in the mail for you for $5 + shipping, I'm sure you'll find a lot of other people that will do the same.
Second, as a shot from the hip, I would say you will probably be okay using that video card, meaning the power supply is probably enough. What card do you have in there now? As far as best performance for the money, I can't answer that as I don't keep up on it, but I don't think its overkill.
A new video card, a newer processor, and mabye a little more memory can have you at least playing some bargain bin games (which is all my cheap parents would ever buy me) with your friends all for the cost of mowing a few lawns.
If you're not 13 and have a real job, then I don't mean to offend you, and you should probably look at a whole new computer.