I'll chime in.
As for the minimum, like others have said anything you buy new can handle it, but might take ages to render. BUT, if you are looking at doing things like multi cam video then the system demands can go up very fast.
AVCHD uses h264 for the video compression which is a motion compensation based codec. So to render a given frame properly it has to refrence all frames since the last keyframe. This means lots of disk read when you are jumping around within 4 concurrent AVCHD streams
http://en.wikipedia.org/wiki/Motion_compensationMy experience was a core i7-920 (Quad, Multi threaded- 8 total threads) , Windows 7 64bit, 8GB of RAM and dedicated video were not enough at times. The big issue for me was disk subsystem performance with multicam AVCHD playback. I was running a single SATA3, 2TB 7200 RPM drive and it was NOT enough. The challenge with AVCHD is, it is a efficient recording CODEC, but not great for the random access to the video stream that editing demands. Frequently when doing a 4 cam video my system would just stop responding when I would cue to another point on the Vegas multicam track. I ended up picking up and converting the entire source video to Cineform and that largely resolved my issues, but disk performance could still be an issue at times even using the purpose built Cineform codec. Dedicated video is not a huge deal even the cheapest dedicated video cards naively accelerate h264 these days. Spending more only improves 3D graphics performance which is mainly for gaming.