It usually depends on the sort of work you plan to be doing with REAPER and how elaborate your sessions will be. Effect-heavy projects will obviously need more memory to run smoother although 1 GB is generally the bare minimum for a 32 bit OS and 2 GB for a 64bit OS.
I plan on capturing my audio on my Akai DPS-24, export the wave file to reaper to mix and possibly add some effects, probably 12- 14 tracks at most, 32 bit Dell. What would you recommend as far as ram? I am at 4 gigs now, dual core. Thanks, Jon