Pom,
Aircraft ownership is fantastic, as long as you have allocated adequate funds, and will use the plane enought to justify it.
Your question is fair and reasonable, and you're going to get good information here. I'll give you some basics:
TTAF = Total Time Airframe = the number of hours it has been in the air since new from the factory. No maintenance will change this number ever. It applies to the whole airplane, until engine(s) and/or propeller overhaul, then those times will never correspond to TTAF again in the aircraft's life.
SMOH = Since Major Overhaul = and can be applicable to the engine(s) and propellor, but not the airframe. If the manufacturer's specified overhaul procedure, and mandatory parts replacement is performed on an engine or prop by a qualified person/shop, the engine and or prop can get a zero SMOH, which is a definate positive, though very certainly drives up the aircraft purchase price that much.
STOH = Since Top Overhaul (or other references to "top overhaul" means the engine cylinders have received major maintenance, but not the "lower end" which is the crankshaft, crankcase, camshaft etc. This work is often accomplished to return to original, the engine's performance, but will not address any proplems associated with "making metal" (wear).
There are other "hours", but for a light aircraft, those are the most important to consider when purchasing.
That said, don't always look for the lowest time airframe in an "older" aircraft. I'd rather buy an aircraft which has an annual average use of 50 to 200 hours, than one which has sat doing nothing for long periods.
I'm much more concerned about the actual inspected condition of the aircraft, than it's airframe time. The two can be surprizingly un related.
That should get to started, but there certainly is more to this than meets the eye. Your questions about purchasing are the tip of the iceburg!