A car that averages 15k miles/year, has a maintenance record, and appears in good condition tends to be less likely to be a lemon than most brand new cars.

For an anecdote, consider that Jeep just bricked thousands of new cars, including on interstates 2 weeks ago.

That GM recalled most 6.2l engines made in the last 5 years; ... Toyota engine castings, bmw chain tensioners, Ford Ecoboost coolant passages, Porsche bearings... Most of these problems became apparent before a long term first owner sold (yes, you should do research)

A pre purchase inspection, and all around maintenance (brake, coolant, oil, transmission oil, and differential oil) will get you a long way; a $2k suspension refresh will take you even further.

Sure, your motor or trans can go out on any vehicle and unless you still have a warranty its your problem.

It sucks if you spend $3500 on a car only to spend another $2000 because the transmission went out and the timing was bad luck. I wouldn't recommend anyone buy an old car I'd they have no emergency fund left after the purchase though.

My wife does regularly drive our old cars. If it dies on the highway we'll deal with it. I don't have a daughter, but I wouldn't worry about my kid driving the kind of old cars I pick up - I'm patients picky, and able to work on them myself. The car would be the least of my worries if I had a young daughter with a drivers license.