Easy now, I know many of you dont like this idea, but if your not going to be using the gun in an illegal way, whats the big deal?
A few things you have obviously overlooked.
1) It is already possible to chase down the chain of possession of a firearm. Once recovered, the agency checks the serial number with the maker, follow that to the distributor, then to the FFL who sold it, and can find the first purchaser from there. If that purchaser does not say who they transferred it to, then even if the gun were registered the trail ends.
2) Registration is ALWAYS step one of any confiscation effort. While they can still track the guns down, the intermediate steps are a form of protection. The moment you allow full registration, you give a list that can be run down if they ever decide to even give gun owners grief (even if ownership is legal).
3) It flat won't stop crime. Period. The person can always say "oh, I didn't even know the gun was stolen." What can be done? Not a single thing.
Sorry, registration or a ban on private sales is not the magic wand to crime reduction that you are looking for. It gives the antis something they dearly love for absolutely no benefit to our side.