This article does a good job of breaking down the bike types. You can get a comfort bike at a store like Target for around $100. You can't get a decent road or mountain bike new for $100 but you might be able to find one used. If you buy used, you'll have to pay for it to be fitted and tuned up.
http://www.rei.com/learn/expert-advice/bicycle.html
I started riding 10 years ago with a comfort bike that my husband bought at Target. It was a surprise and was totally the wrong size, which took M. several non-fun years to figure out. I felt terribly out of shape riding that thing - every stroke was hard and got M. nowhere. Turns out the frame was about 6 inches too small for M.. So whatever you buy, make sure you size it correctly! There are lots of web tutorials that will help you figure out your correct frame size.
He bought a used road bike a few years later that I started to ride as well and I did a triathlon on that bike. It was still a bit small for M. but I was able to put in lots of training miles on it that were fun.
After I decided that I really liked biking, I got a used road bike for $500 that I then put another $300 into having it further custom-sized for M. (had the seat pulled back and changed to a different one, got smaller, more narrow handlebars and a stem that pulled them a few inches closer to M., new gear shifters, finally invested in clip-in shoes and padded shorts, etc. I trained for and completed a 150 mile ride on that one.
If someone had told M. when I was looking skeptically at that Huffy 10 years ago that I'd one day invest in a skinny-tire-and-spandex bike and do 150 miles on it, I would have laughed and laughed and laughed. You never know where your bike will take you!
Anyway...start withe the best bike you can get for your budget *that fits you* and remember to wear a helmet. Happy biking!