Hi, Patty !
The first thing to do when deciding what type of bike you want is to go to your local bike shop.
Most bike shops will allow you to "test drive" a bike as long as you leave a credit card. They expect a customer to want to see how a bike feels. There are lots of snazzy bikes out there. Depending on the bells and whistles, you could pay anywhere from $150- $1,500+ for a bike.
If you're just going to ride around the city, you might consider a comfort or hybrid style bike. Cyclists who do a lot of riding may well have two or more bikes for different purposes. If you're looking to be a bit more fit, then go with a hybrid or a comfort bike. They're both very versatile models.
Don't buy your bike from Walmart or any other retail store, try to buy from a reputable bike shop. Walmart won't let you try the bike. A bike shop will. You need to know how you fit to the bike. Because some bikes look great in the magazines, but when you ride them... something doesn't feel right.
I tried/rode a bunch of different bikes before I decided on a Specialized hybrid. I did paid around $300. You don't have to pay that much. You could find a perfectly good bike for less, but once again it depends on the technology. the more high tech the bike, the higher the price.
If you don't want to pay a lot, consider buying a USED bike. Many bike shops do sell used models for less. That might be a good option too. You can also check craigslist for bikes. But you have to be a savvy consumer. because you could get taken.
Where to start ? Go check your local bike shops. it's okay to look. go online and check out this website for some basics.... www.bicycling.com/
There are many more bike/cycle websites out there. The more you know, the better able you'll be to decide what YOU want from that bike. Don't buy on impulse or you'll end up with an expensive coat rack. Take your time. Buying a bike is an important purchase.