Usually we do a Vet check for a reference and a home visit. Occasionally if the Vet check is really really good, we go with just that. We always take the dog to his/her new home instead of meeting up somewhere, but then all of ours are pretty much local.
For the Vet check, make sure they are up to date on vacs and have regular exams. The vet should be familiar with them, preferably not a new vet. One thing you may also want to check with the Vet is whether the prospective family has had several animals come and go. We've actually encountered this and we're not sure if they are "trying out" pets or what's going on. Just a thought.