How do you purchase your own plane??
A lot has changed in regard to operating costs since I last owned an aircraft but the basic rules don't.
Start with lots of research, as has been said before know exactly what you want and have a good idea of what it costs to operate. Also don't plan on components such as engines/props/landing gear etc, regularly making it to expected overhaul time (especially older aircraft operating on multiple life parts). Have a large contingency fund built in to your costs.
All aircraft are different and even those of the same type may have large variations in fitments/personality which will affect cost of operation. For instance Cessna 152 have a number of different options for engines/carby/mag/prop combination, some may have lower TBO's & higher service costs than others, all for the same (or less) power output.
Anything with retractable gear is more expensive to insure and maintain.
Having a training aircraft online with the right flying school can be rewarding and pay itself off. If it is damaged the insurance will cover it (or the hirer if doing something they shouldn't). There will be increased wear to an extent due to use however under-utilisation of aircraft can lead to expensive problems as well. Don't buy a non-training aircraft (big singles PA32/Bonanza, turbo-charged types and any twin except maybe a PA44) and expect it to pay for itself in this way, it will get trashed.
Get to know an engineer who you can trust to do pre-purchase inspections, they can often find some interesting history in the books.
The Aviation Trader has listings for Aircraft Sales via dealers and private sale.
Banks will loan funds for aircraft best to shop around for best deals and rates. There are also aircraft financing specialists around.
Insurance can be tricky and expensive and varies greatly with planned usage, the aviation trader again has who to call.