beginner bike riders

Hi,
We like riding bicycles in general just around the block,in the school yards and parks. Eventually we would like to try longer distance rideing in larger parks like Golden Gate Park and up hills. We have "regular" bikes,the ones we buy at non-bicycle stores. Can you recommend a few brands with the wheels that don't pop,can go up smaller hills, and rougher areas,have several speeds, and are not too expensive? Thank you for your advise in advance.