Types:

Refractors - If you've seen a pirate movie you've seen one of these classic telescopes.  They have a lens in the front and a lens in the back that you look through.  Galileo used one to observe the moons of Jupiter - pretty much anything that you buy will be far better than what that great scientist had.

Reflectors - Isaac Newton (when he wasn't coming up with universal physical laws and calculus) invented this style of telescope to overcome problems with the refractor.  It is typically a large tube with a mirror in the bottom (instead of a lens at the top).  One looks through an eyepiece on the side. 

Catadioptric - a stubby reflector, but you look in from the back.  The Schmidt-Cassagrain telescopes that I use for public astronomy events are catadioptrics.

Each type is good in its own way.  Expensive refractors can show you a most crisp and wonderful view of bright objects.  Reflectors are cheaper and gather more light.  Catadioptric, probably have the least desirable image quality, but are compact, portable, and wide enough to gather light.

For the beginner who is only going to invest a few hundred dollars, only small reflectors and refractors are available.  Either one is perfect for you.  Intermediate or serious amateurs will have a sense of which is best for them based on their experience and their observing goals.