Whenever someone builds a new computer, the very first thing (after the sort out their voltages, clock speeds, RAM timings, etc...) I suggest they run is Memtest86+ (as you said). Your computer will randomly crash and it will be difficult to troubleshoot if you're unaware that your RAM is corrupted (it is possible for this to happen with a new stick of RAM).
As a plus, you can also run the tool off of a USB key. If you choose to overclock your memory or change the timings, run the test at stock settings first. If it passes, then go to overclock (and re-test it afterwards).
Once that's done, you can use some tools off of the Ultimate Boot CD (which you can coincidentally also run off of a USB key). These include burn-in tests, although I would highly recommend you install an operating system with the appropriate hardware monitoring tools (e.g. HWMonitor or HWiNFO) and then burn in your CPU.
As for burning in the CPU, you can use Prime95 on all CPUs, or you can also use Linpack (used in the IntelBurnTest program). Both programs will definitely give your CPU a run for it's money. Ensure that your computer passes both tests (iterate the test enough times for you to find your system stable). These tools all require you have an operating system installed.