It's great that you are interested in learning about motorcycles! Yay and welcome to the hobby!
The beginner rider course will answer a lot of your questions, get you licensed and insured, and will also let you discover if motorcycling is for you. It's a lot better to make your beginner mistakes on a training range than at 80mph on a congested freeway. The Harley classes cost more, but will put you on a 500 pound, 500cc motorcycle that is realistically capable of street riding. I have done both and both were great.
Cheap is also relative. Budget some money for gear. You will need a few hundred dollars for the basic helmet, gloves, jacket and boots. You can go used for some stuff, but not really with helmets.
As for a bike: I recommend a 500-ish cc motorcycle! They have enough giddy-up to get out of the way of traffic! The Yamaha Virago/V-Star line is one of the most comfortable, easy to ride and inexpensive options out there. If you can find one of those in good shape, you will probably be happy for many years.
Then again, there is a BMW G310R in my garage. It is only 313cc but it makes 34 horsepower, has fuel injection and ABS, looks absolutely fantastic, and costs about $5k brand new, out the door.