I would actually recommend the bike shop, and a not too expensive bike there. I'll explain why. I have found that most people in the US buy and use bikes that are meant more for racing. That means that the person is leaning over to reach the handlebars. If you see pictures of bikers, you'll see what I mean.
However, in most bike-commuting countries like Japan and Europe, people use commuter bikes. These are different, and they do sell them at the bike shops here. A commuter bike has you sitting straight up. Yes, it's less aerodynamic, but that's not the point. Unless you're racing, you don't need aerodynamics. You need comfort. The problem with leaning forward when you ride is that it does terrible things to your back. It causes you to hunch (unless you are very careful), and even worse, it causes your neck to turn in an extremely uncomfortable position just to see where you are going. (you have to look up) Again, look at the pictures. This position causes a lot of back and neck strain for bikers. As a newbie, you really don't want to deal with that. I'm not a newbie, and I don't want to deal with it.
For a new biker (and many old!) I suggest an upright seated style. If you start riding with a bike that has you bent over, you may find the whole set up so uncomfortable that it could impact your feeling of biking. This happened to my sisters, who both picked up biking again in their 30s and 40s, and thought it was tough on their backs. Until they realized their bikes weren't made for comfort. In Holland (big biking country) and the rest of Europe and Japan, you'll see upright bikes much more popular for commuters. That's because those countries are used to having bikes as a part of life, not just as a hobby.
My bike is a Schwinn, not too expensive. (about $350-$400) It has 21 gears, and that's important because it makes the hills easier, a lot easier. Don't get a no-gear bike. And three gears sounds like enough, but if you're new at this, go for some more gears.
Get a bike stand. Lots of bikes don't have them nowadays. You need one, especially as a new rider. It might cost $10 to have them put it on, but get it.
I personally like a basket in front. It's easier to throw in a few things and go. Others like to load stuff in back. Get something. You'll need a carrying stuff mechanism.
And good luck!