Try this while smiling. It's an oldie but goody.
Hi ________. Nice to meet you.
I don't know about the handshake. It is kind of formal for a casual introduction in a non-professional environment. Then again, it could make a BIG impression if you shake using both hands while looking sincerely into someone's eyes. On the other hand, you have to be VERY smooth to pull that off without looking creepy. I vote for avoiding the handshake.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?