I have Canon HF100 and do the AVCHD stuff all the time. IMO beyond the fastest CPU you can get, you will definitely need a nvidia GTX 260 and above. GTX 285 would be nice but according to your budget, GTX 260 or 275 is enough. Microcenter has the 260 for $170 shipped. Buy the Badaboom software too, it's not expensive at all. What it does is to use the video card CUDA function to encode the video in real fast speed.
For high quality stuff to keep, use MenGUI (CPU based), for normal quality stuff, use Badaboom. Compare the result if you have time to do both.
4GB memory is minimum, motherboard will depend on your CPU type.