I've got a 2.4 Ghz with 512 MB RAM myself. You're more than set on those langdoguk.
Perhaps you need to verify your video card supports the various plugins that project64 incorporates. Do some trial and error, checking out each one. Check the audio plugin, and anything else.
You should be able to run P64 as it stands. Also, not sure of all the games' compatibility that you want to play, but many of the mainstream ones should play pretty much 95-100% perfect.