I've bought 7 used cars in my life. 6 of them worked out great. Some of them were for friends, because my friends have identified me as the "how to save money by buying a used car" guru.
3 were from Craigslist, 1 from a mechanic I knew, 3 from Craigslist predecessors.
Whenever I had a professional inspection beforehand and the inspectors liked the car, I got a reliable vehicle. One time from Craigslist, I got a mechanic to look at it informally for free instead of paying for a Detailed Inspection. He didn't like the car but didn't specify his objections. I bought it, suffered $900 of unplanned repairs immediately, didn't use the vehicle much, and sold at a loss, unhappy.
My conclusion: pay for professional inspection, and only buy cars that inspectors really like. Bonus tip: if the inspector says, "How much is this again?" and then says, "If you don't buy it, I'd like to", you have a winner.
Avoiding multiple inspections requires thorough pre-inspection viewing. Screen through the ads as carefully as possible. Yes, there is a time/money trade off. But compared to dealers, my estimate is 20 extra hours of shopping will save you $2000-3000, so probably $100/hr or so for your shopping efforts.
PS. I like the phone suggestion. In general, avoid anything that hints of fishy. Fwiw, here is my routine of so-far-successful procedures (crossing fingers here...)
1. Search just for car types you want in price ranges you can afford.
2. Private party sellers only (fllter out known dealers).
3. Read ads in detail. At all stages, prefer those that provide knowledgeable details.
4. Compare price to kbb.com, exclude prices that are too high.
5. Interview by phone if possible. Text/email, tolerable alternatives but switch to phone if I can. Ask enough questions to determine whether the person really knows the car - thus, screen out dealers. Look for meticulous people who did meticulous maintenance, or had it done. At least you're down to people who know enough to say that. Preference for people whose personal details suggest they have reasons to prefer integrity, fair price and quick sale instead of haggling. Move forward seeking a fair price, not a steal. You want above-average quality at roughly the standard kbb private party price. Usually I shoot for the low end of kbb's range and accept the midpoint, roughly.
6. Drive and test as thoroughly as you're able.
7. If what you see supports the ad, get the inspection immediately.
8. If the inspector likes the car, make an offer. If the inspector likes but identifies small repairs needed, ask for the exceptions' repair price as a discount. Expect maybe half the discount. Walk if you don't have a good deal. If you do have a good one, make a fair offer and close the deal.