I agree 100% with Raxx on this. The basic rules are:
RAM: Enough so your computer can hold your project in memory, and have enough left over to render with, WITHOUT having to access virtual memory (hard disk). A minimum of 1.5GB should be fine for all but the biggest of projects, but the more the merrier.
CPU type (Dual/Quad): As Raxx says, this has no big effect on render times with Anim8or, but may be helpful if (like me) you want to be able to run other applications while a render is underway, without a massive drop in performance.
GPU (video card): The graphics card is only used to display simulated materials in the workspace, and has no effect on rendering whatsoever.
CPU speed (GHz): This is about the only thing that will actually speed up the rendering process, assuming there is sufficient RAM and nothing else is running. The faster the better.
My advice would be to talk to your local computer shop, rather than one of the big retailers, and advise them what you want the machine to do (bearing the above points in mind). They should be able to provide a quote for the parts, and in my experience you can often get assembly thrown in for free. A custom built machine like this can be as much as 30 or 40 percent cheaper than an off-the-shelf unit (at least that is the case in Australia), and if you are happy to recycle things like monitor, drives, graphics cards, keyboard, mouse and case/power supply you can save a bundle.
NOTE: Be careful with the power supply, there are a couple of different cable hookups and older power supplys won't work with more modern motherboard/CPU combinations. Power supplies are cheap anyway, and most of the new ones I have seen have connectors that can be adapted to suit both old and new motherboard/CPU combinations.