AVCHD is highly compressed and requires a lot of computing power to edit on the fly. If you are going to end up putting the video onto DVD, then the best way of doing this on lower powered equipment is to transcode to another format such as mpeg2 or mp4 at DVD resolution (720x576). This can be edited in all NLVE's such as Vegas with ease.
For transcoding try:
Tmpgenc 4.0 Xpress (about £50 but very good and allows adjustment of things like noise, sharpness exposure, saturation etc)
Nero 8 or 9
Handbrake (free and excellent) transcodes to mp4.
WinFF (Free)
On the command line ffmpeg is quick and efficient.
p.s. I use a 3.1 GHz quad core Q6600 intel processor and it handles this work with ease. If I want to do editing for a product that is to remain at HD resolution, I still transcode to mp4 as it requires less processing power (but takes up more space). However, rendering at HD resolution is still close to real time. I don't think that you need an i7 processor but if you can afford it, why not.