I've only ever sold privately and as long as you take sensible precautions it's a good way to get a better price for your car. My son had 4 guys turn up all together to buy his car and he immediately sensed something was wrong when they tried distraction techniques so they could put 'faults' on the car. He told 3 of them to go away which they did once he'd let them know he was an army officer and any nonsense wouldn't end well.
I keep all the documents indoors until the prospective buyer has satisfied himself with a visual check and I've taken him for a test drive (me driving). I ask if they want to see anything particular during the drive, harsh acceleration/braking, speed etc and choose a suitable route. I then let them drive but only for a short while on a quiet part of the route. If they drive your vehicle their insurance is almost going to be 3rd party only but it's worth checking they have it.
After the test drive I lock the car and leave them to admire the newly polished paintwork while I get the MOT, service book and the V5. Then the fun starts, have a firm idea of your lowest acceptable offer and don't go below it. If you get the asking price you've put it on too cheap 🙂
I sold my IS250 in December and accepted a bank transfer which was done on the spot in 2 payments. Bank apps let you check that the money has been received almost instantly. I don't really like cash especially in the evening as the buyer (and anyone he talks to in the pub later) knows you've got a few grand indoors overnight. Once the cash is in you can complete the relevant section of the V5, hand over the buyers part and the other docs then post your bit of the V5 when convenient.
I'm not saying my technique is perfect but it's worked ok for me and I've sold possibly a dozen cars this way without incident. Hope it helps