The result of proton-proton fusion is a diproton, or He-2, which is extremely unstable and thus this is not a viable fusion reaction.
In fact, there is no way you can use only individual protons as fusion fuel - you must have SOME neutrons in the mix. However if you have extra neutrons, they will end up producing neutron flux which will irradiate and activate the materials it hits.
If you use Tritium-Deuterium fuel cycle, you can line your reactor walls with Lithium-7 which will produce tritium under neutron bombardment; this would mean the reactor would replenish its tritium from its inner walls, which would have to be replaced from time to time. Regardless, neutron flux is not exactly ideal if you want to eliminate radioactive waste products.
There are two fusion reactions that produce no neutron flux (well, to be sure there are more but these two are the easiest to accomplish): Helium-3 - Deuterium reaction, and proton-boron reaction. Of these, the former is easier to accomplish (lower optimal energy level to initiate the fusion) but the fuel is sparse (Helium-3 is rare isotope on Earth), and the latter requires about 500 times more powerful confinement to run the fusion reaction at the required, high temperature, but the fuel is practically unlimited - hydrogen is plentiful, while boron is a reasonably abundant element. The Tritium-Deuterium reaction also offers about 2500 higher energy density than proton-boron reaction...
There is a third aneutronic reaction achievable with light elements: proton-Lithium-6 reaction, but its energy yield is rather pathetic.