Ask for maintainence records. Look for the number of owners. How long has the latest owner had the car?
What you need to know is, when were the hoses/belts/brakes/batery replaced last. In a 150K mile vehicle, they all will have been replaced at least once. If not, they will fail soon.
For cars that have a timing belt (you will need to google the specific engine for the specific model you are looking at), when was it replaced last, what is the recommended change interval?
Same thing for the alternator and power steering pump. at 150K miles, if these haven’t been replaced, they may be nearing the end of their lives. Automatic transmission? If the fluid has been changed in the past 10,000 miles, try to find out when it was changed before that.
Cars with over 150K miles are not necessairly junk if the previous owner has maintained them. The perfect one would be a single-owner vehicle that has been only serviced by the dealer. Those are rare. A two-owner vehicle where the 2nd owner bought it with 30-50,000 miles when it was 3 to 5 years old and has kept records on the maintainence since it was bought is nearly as good. You really want to find one where the owner has kept the maintainence records. DIY oil changes are fine, but I would want to see how the owner is keeping up with the change interval. FYI, I keep all this information on an excel spreadsheet on my vehicles. I may not have all the receipts, but I do have a complete record of when the windshield wipers were replaced.
Of course, as has been said, any oil, coolant, gas, or power steering leaks are bad news. A reasonably clean engine, not spotless, is also a good sign. A spotless engine is suspicious, but one that has oily build-up in easily cleaned areas, but is neat and not obviously wet with leaks, is an indication that they are not trying to cover up a problem.
You might be better off buying a car nearer the higher end of your range if it has a good maintainence record. My “fleet” of cars consist of 3, built in 1980s-1990s. The lowest milage one is at 150,000, the others have over a light-second on them (186,000 miles to non-geeks). I would take any of them on a 1500 mile road trip without a second thought (other than a tire rotation). But, I am very familiar witht the maintenance records of all of them.
excavating (for a mind)