I use a single edge safety razor. I have a very coarse beard ( yes, it gives good back rubs), so coarse that I can't grow a beard because it cuts into my baby soft face. I have the worst combo, sensitive skin and a coarse beard. I use old fashioned shaving soap with a badger brush. Shaving oil is awesome as well. I get an incredibly close shave without ingrown hairs.
Just buy an old one from an antique shop. You can get blades from EBay.
DD