I've only ever bought used cars, from individuals. Paying extra for the overhead of a dealership and some salesperson's bonus seems absurd to me. You're pretty much guaranteed to get taken advantage of by a professional.
Local classifieds, private sellers, take the car to a trusted mechanic for an inspection.
I've never bought a car at a dealership, and neither has anyone in my family in 25 years. But then again, I know cars inside and out (even from before my car sales career) so I feel pretty safe not accidentally buying a scammers car from Craigslist.
Very few franchise dealerships would ever sell a car with problems knowingly. It does happen, because people trade in cars with intermittent problems without telling the dealership.
Compared to Craigslist where there is no shortage of people selling cars directly with current problems, intermittent problems, hidden problems, and massive paperwork issues that can stop you from registering the vehicle all together until resolved.
This only leaves the potential for massive paperwork and back due fee issues. Surprisingly common on craiglist. A spare current registration sticker gets slapped on that belongs to another vehicle of theirs, and you buy the car not knowing it has 3 years back due fees totally $1000, probably approaching $2k if it's a pickup truck (atleast in California).
Personally I've never paid more than $7000 for a car.. but yeah, a cheque, or a transfer. You transfer the ownership at the govt office, and it's done.
Dropping 30k on a car seems a little nuts to me, but I understand different people have different values.
Local classifieds, private sellers, take the car to a trusted mechanic for an inspection.