I run a minecraft server myself so i'm experienced with this.
Any dedicated graphics (amd or nvidia) found on a modern system should be fine. One of the most important elements will be running 64 bit java.
I have a 2-3 year old notebook athat never drops below 30 fps in minecraft. heres it's specs.
core2duo 1.8 ghz
4 gig's of DDR3
nvidia GT320M with 1gig of dedicated graphcs memory.(low end)
500gig hd, wireless n, 15.6 inch screen, Asus K50I low end business notebook
cost? $600 Canadian. I know its not easy finding a suitable notebook with dedicated graphics for 500$ but i bet if you look hard you can find one (before taxes at least)
plays minecraft full screen on Graphics : Fast, Render distance far, particles all never droping below 30, averaging about 45 FPS.
I only use my notebook as a secondary computer, but I have spent many hours playing minecraft on it just fine, therefore I imagine ANY modern recent dedicated memory (doesn't share system memory) nvidia or amd gpu would be fine.
EDIT : This is basically an modern updated version of the notebook I have spec wise : http://www.ncix.com/products/?sku=65174&vpn=K53SV-DH51&manufacture=ASUS&promoid=1263
its selling for $724.99 canadian right now, which is expected because of the state the economy is in, if your willing to take a hit on your screen size , processor and ram, you can get a still decent one for 600$ : http://www.ncix.com/products/?sku=65173&vpn=U31SD-DH31&manufacture=ASUS&promoid=1263