Another thought on the aircraft. $20,500 is a bit high with the paint and corosion issues.
You have some room to negotiate and since the annual is due, doing the inspection/annual as a part of the buy is additional leverage for you.
It depends on how motivated the seller is. The missing logs books are another concern. Get the history of the engine and the paper work on all the ADs. Just because they say it was done, does not prove it was done. Hopefully some of the info on the FAA CD history will help. Find out what shop worked on the plane and who owned it before. Even with the log books missing, the shops who did the work should have some records.
What you are up against here is the "emotional buy", and that is not a bad thing, but it does not have to cost you more if you do your homework. You have been infected with the "flying bug" and it is terminal.
"You can't loose what you don't have", and with a line of credit approved you can afford to shop around.Just don't drool in front of the seller, that will cost you $$$.
Please don't take this as that I'm raining on your parade, I just don't want you to make some of the past mistakes I made.
Good luck, and congratulations on your journey to the PPL.
John