If your budget is restricted and using ICF's recommendation then even the cheapest of the PCA computer list would suit your needs Click Here although for faster video rendering I would upgrade the RAM to 8Gb and make sure that it comes with the 64bit version of Win7
I have used various versions of Power Director with no problems. My present PC is an HP Pavilion 2-3 years old. My previous XP PC was 12 years old and also was OK editing and burning discs.
Any reasonably fast PC should be fine.