I have bought two planes and you learn a little more with every purchase.
A prebuy or annual will double check the required ad's are complete but will not necessarily test all the radios and avionics or other accessories on the plane. Fly it and use every thing for yourself. Slow cranking can indicate a dying battery or need to rebuild the starter. No doubt the owner put a quick charge before you get there so if it is anything less than spritely starting you should suspect some hidden costs although not significant costs. Starter rebuild is $200 or so and a battery is $200-300 but why should you pay for it?
Mag drop that is not within 50 rpm could indicate one or both mags require IRAN that is another $500 ea. Could also indicate carburetor problems $650.
Even if you are not a mechanic you can read and understand every single line and every entry in each of the a/c, engine, and prop logs. Every entry should make sense. If anything doesn't make sense query the mechanic and owners about it. When asking questions watch the body language more than listening to the words. There are plenty of free sources on google for reading lies.
The Cherokee series is a straight forward airplane with few issues. However the issues have AD's. One, I can think of is the hollow core crank case has an AD for corrosion. Once inspected if corrosion is found then it must be redone every year or 100 hrs until you rebuild the engine. This is an extra $200 cost during annual, every year that you do the annual and it might well prevent you from getting to TBO or past it. So I would avoid any with found corrosion even if treated.
Be careful about any work done on prop. Lycoming requires a tear down of the engine for any prop strike, even if by tall grass on a runway, if it slows the RPMs of the engine. Many, many might illegally ignore this but not reporting it to the mechanic and getting him to treat the prop without requiring the lycoming break down. So if you see work done to the prop make sure you understand what caused the work to be done and why wasn't a engine inspection performed?
Dot your i's and cross your tees going through the purchase process and then relax. There is no plane I would prefer to buy than a Cherokee from the risk standpoint.
Here is one area that many guys get caught on. Even a 500 hrs engine is considered run out if it is older than some number of years. I think it is 15 years or might be only 13 years. Owners will tell you its a strong engine and that might be true but for purpose of valuation it could be a run out engine. Do not ignore this as if you unexpectedly have to sell the plane sooner than you thought it will be you trying to convince some one else that your engine is not run out.
You've already picked the plane so this next bit of advise is for everyone else or if your still debating a purchase. There is no way to guarantee that a low time engine is in the perfect condition or hasn't been abused (that you are paying top price for it as if it is perfect). So I prefer to buy a high time engine which lowers the valuation and purchase price of the airplane. I will either then rebuild the engine at a shop beholding to me for warranty and know what I am getting or monitor the engine and get free hours as I fly it past TBO. Both are good value propositions to the owner. Buying low time new engines is the opposite proposition. There is no way for you to make out on it and there is every chance that you could buy a lemon in which chase you have to pay for the engine twice, once in the higher inflated purchase price and once again when you have to fix the engine at extremely high costs to you after you own it and discover what wasn't done correctly.
I would think a good appraiser knows this but confirm that if your model aircraft came with a IFR radio and wing leveler from the factory that it still has them or upgraded better models. If they were inop or removed and not replaced you may need to deduct $10k from the valuation to replace or fix the inop or missing equipment.
good luck.
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