Most of my cars have come from eBay with a buy-it-now price. Never had any problems with it. I did recently sell my car through AutoTrader but it was listed on eBay as well - it just went to a guy from AutoTrader first.
I've not bought or sold a car through Gumtree, nor Facebook marketplace. They're all much of the same really. You need to do the same checks that you would with any second hand car - do an MOT history check to make sure it's been looked after (occasional advisories on normal wear and tear items OK, constant fails on major issues is bad), as much of a service history as possible, and make sure you have a good look around the car and take it for a test drive. Take someone with you who's more experienced for the test drive/prod around the car.
Occasionally you'll still end up buying a heap. I managed it once, but I think it was bad luck rather than a dodgy seller.
I bought my Passat with no test drive, with no service history, and probably with a kind-of dodgy MOT. It ended up being an amazing car that I put 30,000 miles on before selling recently. Sometimes the stars align and it all works out for you, but you're best off doing everything you can to make sure you don't buy a pile of poo.
Another good tip is to look up known weak spots on that specific vehicle. It helps to massively narrow down the main things you're looking for when prodding around the vehicle.