All of these guys have given you good information. The biggest mistake I made with my first bow was that is was a little too long for my 80% ground, 20% tree stand hunting. I now have a mathews SQ2 that is perfect for my hunting style. Look at some used bows as well, you can sometimes find a better bow for less money than a cheap new bow. Most of the time they already have the accessories on them almost ready to shoot.
2. It must fit your hand. Many of the bows that I pick up just feel like a piece of equipment, it should feel like an extension of your arm.
3.Don't worry about arrow speed. All of today's bows are fast and accurate if you set them up right.
4. Use a release (and a string loop on a short bow). A wrist strap style is very helpful and functional.
5. ***Get a whisker bisket arrow rest. The arrow can't fall off the rest.
6. If possible find a bow that has multi-directional string (zebra string or similar) so that you don't have to use anything to keep your peep site from rotating.