I have just bought a Permit to Fly Aircraft (my first purchase) - still not delivered yet.
The log books etc are more less the same as for a full CofA aircraft. Airframe, engineand (in my case) prop (variable pitch).
I checked all log book entries against work records and that all hours totalled correctly (there was a discrepancy of 20 hours on the engine log book but that was discussed, corrected and counter signed by both the current owner and the LAA inspector).
I did not take the LAA inspector with me but he visited after I had made an offer (subject to his inspection) and got a report from him. I also required that a new permit to Fly was issued prior to purchase (only 2 months left on the old one).
I checked all mandatory modfications had been carried out - both physically checked (where possible) and signed off in Log book by LAA inspector.
Had a trial flight - about an hour and checked general handling, power-off and power-on stall behaviour as well as climb rate, ASI calibration with GPS etc.
Gave the engine a good once over with covers removed and checked all cables, pipes etc. for chafing, wear etc. Give the tyres and brakes a good looking at. A good guide is the general state of the aircraft - does it look like it has been well cared for (scuff marks, dints and dings, cleanliness, prop chips etc. etc)
I made sure any specialist tools were included in price as well as covers, any spares etc.
Had a long chat with current owner about his time with aircraft and why he was selling - made sure it all "stacked up" with log book entries etc.
Hope this helps