I've bought off ebay, including my current Porsche,
You can do a fair bit of background before you go and look,
Ask for the Reg No, then you can do an online HPI check, cost around £20 and will tell you owners and any
Insurance or stolen/recovered issues. you get the result emailed to you immediately
Sometimes an HPI check shows more owners than the seller is declaring, but this can be just the adding and removing of private plates, my log book showed 3 owners, the HPI showed 6, cos each one put their own private plate on.
Ask for a scan of the log book, Tell the vendor he can mask off all but the last 4 digits of the VIN and engine number if he's worried bout identity theft etc, this will tell you on the front of the log book of any write-off history and let you see the log book to cross check against the HPI check.
Scans of old MOT's may show consecutive mileage and dates etc.
You could ask for scans and emails of the service book and ring a couple of the dealers in there to check they did do the work, certainly the last major service stamp.
These won't give you any guarantees of course, but should start letting you know if something smells a bit fishy if things don't cross-check etc etc.
If the vendor says he can't be arsed to scan & email, that of course could possibly be another warning.
But the final thing of course, in any purchase, Caveat Emptor !!
I was very lucky on one of my ebay cars, and reasonably lucky on the other so it isn't all bad news, (but it can be) lol