I can get this game running full speed on a 1.2ghz system using 1964. I believe you need at least a 1.4ghz to get decent speed on pj64. You would also need a decent gfx card to get good speed and at least 256-512mb ram.
Well more in the way of a pretty good video card. As long as you've got at least a Pentium 4 processor and 256MB of DDR RAM, you're ok there. For video card, something with at least 64MB RAM I'd say. I'd recommend a geforce 4 Ti4600/ATi Radeon 8500 or up. You should be aware though, there are some graphical errors on the rom version so don't expect it to look fully the same as the N64 version.... well at least on my system there are.
It doesn't matter if you have a pentium 4 or not as long as you have a 1.4ghz processor to play it on pj64, and as for the graphics errors, there isn't a way around it yet, but they are very small errors so it won't irritate anyone too much.
I am happy with the near perfect (in my opinion) peformance on 1964 with my P4 and Geforce 2 MX. Sometimes, it really comes down to plugin configuration.
Goldeneye barely runs fullspeed on my 1800+ system with PJ64, so get the fastest processor you can get away with! It helps a lot for the games tha run slow.
My 1.4 Centrino (laptop) can crank out Golden with no slowdowns. Of course the 512MB of ram and the Geforce4 GO 4200 may help. Also, I hear the 1MB of L2 cache also helps...