Before I sold mine recently I had everything running beautifully on an old Pentium II with 256MB ram.  It ran even the most power hungry games like the Street Fighter Zero with no discernible probs.  Any vintage P4 would be absolute overkill - UNLESS!!! you are going to run PinMAME & Visual Pinball, then get a good P4 dual core with 1 gig of ram and a reasonable video card :)