I have done these sort of deals. What you're buying also matters as to how you go about it. I'll explain.
Most classic cars I've bought were done remotely at first. I locate the car, talk numbers, and proceed with the buying process. The first step is to write up a simple contract. It doesn't need to be a full-on legal document. Just something that says your name, their name, and that you are putting "X" amount down to hold the vehicle for 5-7 business days as you secure funding and validate the car. On classics, I always find a local repair shop with stellar ratings. I wire them a fee and they go and inspect the car for me. If it's a high dollar, ultra rare car, I will go myself and/or bring along an expert to check the provenance.
But, for normal modern cars, I just do the simple contract, pay to get a mechanic to look it over, and if all is well and good, I will pay the buyer in their desired format. You can do bank wire transfers, mail a cashier's check, PayPal, etc. As part of the buying process, I will also send them a bill of sale to sign. On that bill, I list things like, "Buyer agrees to make the vehicle available for transport pickiup at (date/time) for (delivery service). Any and all personal possessions left in the vehicle are not guaranteed to be returned, please ensure you remove all personal items and leave all keys in the glove box."
The delivery driver will arrive to pick it up. I usually have the driver facetime with me and I have them go over the car to make sure they didn't do things like replace custom parts with things not shown in previous images. They then evaluate the car for visible defects and note it on their manifest. This is important as anything wrong with the car that's not on that manifest becomes an insurance claim against them when they drop it off.
I've done this quite a few times and I've never been burned by a remote deal. I've shot down quite a few after a mechanic does their thing and found unreported issues. However, I have never bought a car and had it arrive in a state I wasn't prepared for. The only recurring issues I have had revolve around crap left in the car, hence why I now put the disclaimer in the bill of sale about taking their things out of the car. I've had issues where people swear they left something in it that wasn't there, wanted the return of heavy items that they didn't want to pay shipping for, and so on. This doesn't mean I won't mail a guy's wallet back to him, but it gives me the option to clean my hands of it if there is a major disagreement or undue hassle in returning the items.
