I have never owned a car or been to a mechanic...for anything.
Yoikes, ok then
Find one *really* recommended, that you *really* trust, otherwise you run a serious risk of handing them $100 for an inspection and having them laugh maniacally while they come up with a long list of things that may or may not actually need replaced/repaired
Just look up reviews in your area :)
You can take it in for an inspection, mostly of wear items like brakes and belts, though you can also inspect those yourself pretty easily with a little learning. Look up the manual for the car and it will have a recommended list of service items.
IMHO the best thing to do is take it on a LONG test drive, hit potholes, climb steep hills and brake hard, you've hopefully been in enough cars to tell when one is falling apart or doing something very not ok, like squeaking wheels, pulsing brakes, steering pulling one way or another, not shifting, etc.
Common items -brakes tires, belts, shock absorbers, door locks if you need those (debatable), automatic transmission not operating smoothly (pricey that one, but often hard to tell)
Tires can be an unexpected $500 gotcha, check the tread and also the date code, they expire after a few years