You don't need a high spec machine, I'm assuming you're not doing high end work yet?
I learnt 3D fine on a 700mhz single core with 128mb of dedicated graphics RAM, if you just modelling with polys and doing simple renderings you will be fine with a gaming computer. As Gen said a dedicated graphics card is the most important for running a 3D app smoothly.

If you learning then some insight into what you will be doing will be useful, if you're going to be doing heavy modelling or texturing then a graphics card with alot of memory would be a good idea. If your doing complex rendering (lots of raytracing and indirect etc) then more processer power is going to speed you up.

If you doing heavy renders with lots of geometry then the more RAM the better, 32 GB ish is a standard for a render blade.

If you're doing effects or other super heavy work then get as much of everything as possible.