I've bought one or two LPs from Amazon, but over a hundred via Ebay. I haven't had any issues with either route. Both Ebay and Amazon have good mechanisms in place to deal with problems, and certainly for Amazon, "the customer is king".
As with watches, so with second-hand LPs, the greatest risk is in the definition of condition - one persons A1 may be another's B-, so as always, "caveat emptor".