First, I agree with knox. Didn't you test drive the car and get it checked out by a mechanic/knowledgeable friend ? Also engine cleaner and a garden hose work pretty good. Extremely dirty area might require 2 applications.
All the "tune up" things you mentioned are regular maintenance items and if them have never been done, you should take care of it. Will it solve your proble ? Maybe. Most large auto parts store will pull the Diagnostic Trouble Codes (DTC) for free.
As for your transmission issues, pull the dipstick. If the oil is dark red/brown (not bright cherry read) and/or is smells burnt your probably going to need your transmission rebuilt soon. If it is an electrical problem, the DTCs will tell you. | 
