I'd say too that it's fairly typical to play on the second date. Generally there won't
be a second date unless there's interest from everyone involved.
Still, you have a right to your preferences and if you need a few more meetings to feel comfortable, that's OK. Just make sure that you communicate that along the way. Sure, you'll find those people who won't go along with that, but I believe that you'll also find those who will be patient. After all, you're worth it, right?
-B