The trick is to always be polite; let your child know that they are always welcome to invite their girl/boyfriend to dinner or family events.  When a specific occasion is coming up, ask if they would like to invite the friend or not; make sure they know that the invitation is being extended because the person is important to your child (definitely NOT because she or he is important to YOU).  Then the choice is theirs, and they know that the invitations will be there whomever they choose.
Dating is to try out new people; see how you mesh with different personality types.  You really don't want him spending the rest of his life with the first person he started dating at 15, do you?
We've been through a variety of boy & girlfriends between all six kids, and some were better than others, but almost all were pretty decent kids.