Hello and welcome to the forums, it's a great place here and I'm sure you'll have plenty of advice to help you make a choice. As Savra mentioned, what you want to accomplish with the bike, the kind of riding that you will want to do would be the biggest factor in what kind of bike to start with. How much you want or have to spend on it is another factor and advice here can help you get the most bang for your dollar.

You mention you will be riding in a hilly area, you'll want to have a bike that factors that in with lower gear choices over top end speed choices. I started out with a 7 speed comfort bike and within less than a year I've moved to a hybrid bike that combines the comfort of a cruiser with the low end gearing for mountain bikes that makes hill climbing much easier and possible.

For advice I'd choose a bike from a bike shop over a department store and if you are constrained by budget I'd choose a bike from craigslist where you can get better value for your money. I'm not dogging department store bikes because I am certain that my first bike from craigslist came from a dept store. I just wanted to be sure of two things 1) I would continue to want to ride before I invested a lot of money and ensure it was not a passing fancy and 2)I wanted a low entry cost until I could see what kind of bike riding suited me best. Havings said that I got what I wanted from that arrangement. It worked out great.

Seeing that I will be riding much more than I had anticipated, things like a quality bike and better components began to mean something to me. If I had jumped right into a higher end purchase I probably would not have bought the bike I just recently did, for me it worked to have time to sort things out.

If you've had some recent experience with cycling before your knee surgery, perhaps you already have an idea of the style of riding and what feels good to you and it may make your choice easier and you can go for a better bike right out of the chute. Test ride several different kinds of bikes, it really helps a lot.