You would be looking at an HD 7770 (which in the linked article had the best Performance per dollar) or around that level. Make sure you pick one with GDDR5. A 2GB DDR3 will not run faster than a 1GB GDDR5. Here is a list
of GPUs and reviews from Tom's if you want to find something around HD 7750 - GTX 660 kinda level.
Minecraft does not require huge GPU power and can be quite CPU (sometimes RAM) demanding with mods installed. I am currently running 35 mods including Buildcraft, Galactica (Moon and Mars) and various othe industrial type mods and I cannot keep the game running smoothly unless it runs in multicore chunk updating (from Optifine), even though I average 90 - 100FPS with the mods running.
To be entirely honest, I used to run this game on a laptop with an i5 420M, 4GB RAM and a Nvidia GT 230M (1GB). It would run everything on High (except normal render dist) and would not lag often, unless spawning new chunks/large number of entities or jungle biomes which can be graphics related issues, but the CPU would be nearing 100% usage when the GPU was only around 70 - 80% 9this was on one core before the mods were installed).
TLDR; you will need to have a pretty balanced system, but the HD 7770 or equivalent should be good for most things this game has to offer (vanilla that is). You should be able to run some higher res texture packs, but I don't imagine you will get past 256x256.