Hi
1) I do not think you'll notice any big difference in 128 and 256 MB memory. What I consider important is if the memory is 64/128/256 bit architecture. Cheap memories can really kill performance.
2) I recommend GeForce - Nvidia is my personal favourite as a company. In the budget selected by you there's probably a NVidia FX6600GT available (or clear 6600 without the GT it's cheaper - about 137$ in Bulgaria so it should be even cheaper out there).
3) Videocards are with DDR RAM even yours Ti4200 is (a great card btw)
4) Search for tests, benchmarks of the selected card. Google for the name of the card + the word "review" (or benchmark, or test) + the game you need.
~HERE~ - a Google search for 6600+benchmark+Doom 3 for example
Cheers