New graphics card for non demanding games

Alright, I am looking for a new graphics card for my crappy pc that I have had for a number of years. I am a casual gamer that usually plays non demanding games such as Minecraft or TF2, so I am looking for a medium graphics card. my concern is if my computer will be able to handle such a graphics card.

comp specs:
2gb memory (dont laugh)
processer: Intel core 2 CPU
32 bit
current graphics card: Radeon x1600

Pls tell me what kind of graphics it could handle
 
I'd say any of the current $100 graphics card would work. But then I don't know what size power supply you have.
 
With a 365W, it would probably be best to stay under $100. Choosing anything over $100, I'd recommend a 400W or better PSU.
 
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