That RAM is DDR2 and that motherboard uses DDR2 so you're fine there. That kit is 2GB btw, I'm assuming you bought two?
Micro ATX motherboards fit just fine into regular and full tower cases... the question is, did eMachines use some weird custom case that's only compatible with their own parts. The T3612 looks like a typical micro ATX case... I can't say for sure though.
I think the gaming performance will be pretty good. I mean, you're not going to be able to run GTAIV at highest settings on 1920x1080 and get 100 FPS, but I think you'll be satisfied with it.
My current PC is similar in the price of the components and the video card, as long as you're not one of those people who needs all the detail settings on Very High then you'll be happy with it. And if you were one of those people, you'd be spending $300+ on your video card, so my guess is you're not.
Personally I think it's a great idea to build with around this price range... a $100 video card is worth like $70 after a year... a $300 video card is worth maybe $125.