Location, location, location
You listed Seattle, but are you a legal resident of WA? And is your father? Or are you legal resident somewhere else. it makes a difference. In WA there is (currently) no paperwork requirement for transfers between private individual, providing both are legal residents. It is prudent to get a bill of sale, of course, and the seller needs to see ID (proof of residency, etc.) but between father and son, this hardly applies, and is just good sense, not a legal requirement.
For example, if you are in the military, and your home of record is WA, then you are a legal resident, no matter where you are stationed. On the other hand, if you go to school in one state, but your home is in another, it can get tricky, depending on specific state laws.
Your post makes it sound like you father does not live in WA (because we don't have a long "purchasing process"). If this is the case, then I have no advice for you, other than to check the laws where he lives, and comply with them.
Then there is the whole "straw(man) purchase" thing. BUT, buying a gun as a gift is allowed. Again, check the laws that apply to where the gun is being bought. Most dealers can give you the correct info (otherwise they won;t be in business long).
A bit more info on your situation would allow a more concise answer.