If a person to person sale is legal in your state without an FFL dealer performing a background check, that would be the best way to go about it. Contrary to popular belief, very few states have "registration" of handguns. But if by registration you mean that no 4473 is filled out, etc. a private sale is the way to go.
Should you want to build your own, the receiver or frame of the firearm, unless sold in a legal person to person sale needs to be processed through a FFL holder.
I agree with the legal person to person but I know that for me, I am going to get a bill of sale if I ever sold a handgun or long rifle to cover myself down the road. I don't want the ATF coming to me one day talking about this gun in my name blah blah blah...I want proof if I no longer own it so though you may purchase it from a private person, they may still ask you to sign a bill of sale so that they have evidence that they no longer own it.