First Bike Ride

Mia had her first bike ride in Hilton Head. We rented bikes with the baby seats on the back and rode around the neighborhood and to the beach every day. She loved it. We'd say, "Mia, do you want to go ride the bicycle?" and she'd go to the front door. I was a little worried about it at first, but our neighborhood in HH was nice and flat and there weren't a lot of cars. The thing she didn't like was the helmet, which looked totally hilarious on her. It was too big and would fall down in her face. So, by the end of the week, we let her ride around without it (gasp!). I'm thinking of getting a bike to ride around here. I want the granny kind with the wide handle bars - like the one in these pictures. But, I need gears. Any suggestions? I know nothing about bikes.