A mountain or a comfort bike would probably be a good choice for you. They both will have easy gearing so you can take it slowly on hills, and not have to push yourself too hard. A mountain bike with suspension will have a softer ride along with the easy gearing, but they will be heavier.
The comfort bikes, or hybrids, are usually meant for a mix or road and dirt trails, but are more road oriented and lighter. The comfort bikes often have a suspension seatpost, more cushion to the seat and a more upright position which you might find more comfortable and cause you less discomfort.
I agree with paradesgoby that a beach cruiser would be good as well, but if there are hills where you want to ride, keep in mind that the beach cruisers have no gears.