I also agree that a 17" iMac would be fine for you.
If you are a serious gamer, then I would definitely consider upgrading the graphics card and upgrading to 2GB Ram which will put you over your budget.
If you are on a budget and want to hook up your display, then you may also want to check out a nicely upgraded Mac Mini. You will not get as fast or good of a processor (2.0 Core 2 Duo on iMac vs. 1.83 Core Duo on Mini) but it should suit your needs within your budget.
On the Apple store page is a "Talk to Us" button to open up a chat window with a rep. You can call them too. THey are really helpful and don't push upgrades. I had three of them tell me I didn't need the faster processor or graphics card on an iMac.
However, the lower power you have now, the sooner you will be throwing the thing away to get a new one.