I have bought a number of aircraft over the years and helped others in the purchase of theirs.
Once a decision has been made about what you want the aircraft to do (is it for touring, VFR or IFR, farm strip visits, aerobatics, number of seats, etc) and you have found the aircraft which ticks all the boxes then the first thing for me (after of course the visual inspection and check on its flying paperwork) is a test flight (assuming it has a current permit or CofA) I normally try to fly the CAA test schedule dating back to the days of Star Annuals, its structured and helps you not miss anything. It's surprising how much information such a flight will give you in terms of how the aircraft is performing, how well it climbs and what it stalls like (is it rigged correctly etc)
It also allows you to systematically check everything works, and if it does not it gives you room to negotiate with the owner. I would normally then go through the log books and see if anything obvious jumps out at me.
If the aircraft still looks worthwhile I would then invest in an engineer going over the log books and aircraft for me.
I have never had a genuine owner object to going through this process, if the owner does object then walk away - he is perhaps trying to hide something from you and it may well end up costing you a lot more than anticipated.
A good starting point for the test flight is reading~:
http://www.caa.co.uk/docs/1455/Check...-April2009.pdf
Just remember, the flight is for your information only, its to give you some idea of how well the aircraft performs rather than as an official test flight. The use of the schedules gives you some method in how you check the aircraft. If you don't feel able to fly the test safely to the suggested limits through experience then get a more experienced pilot to do it for you and go along as the observer
If you do the test flight schedule accurately, (then if you buy the aircraft) you will have some baseline figures for performance and as time goes on should the performance decrease in any way you will be able to quantify the change and it will help you and whoever maintains the aircraft decide what remedial work or investigation (if any) needs doing.