Film Single Lens Reflex Camera (SLR)
Many photographers started with a manual film camera like a Pentax K1000 or Minolta SRT201. While manual film cameras are not just limited to these two models, they embody all the features of a good student camera. Everything is manual from focusing to exposure. Students who start with these cameras learn how changing the shutter speed requires a change to aperture to achieve the proper exposure.
Digital Point and Shoot
If you want an easy to use camera that will make the decisions for you and give you lots of options, then today's digital point and shoot cameras are for you. These cameras will do everything from focusing, setting the exposure, changing the white balance, and do so with the photographer only having to push a single button.
Digital Single Lens Reflex Camera (DSLR)
If you want more control and the opportunity to use different lenses on your camera then a DSLR is the way to go. DSLR's usually come in three different levels. There are entry-level models, mid range or "pro-sumer" models that are similar to entry level but will usually have a sturdier body and may incorporate some features found in the third category of professional models. In each class these cameras can be set in full automatic mode or full manual mode. And all of them allow you to use different lenses.
New or Used
If you are buying anything other than a professional film camera, then it will likely be a used model. The good news is they are inexpensive. The downside is if you need to get them fixed it can cost you more than what you paid for the camera. In DSLR's you can buy a DSLR that is two or three years old, for roughly a third of what they retail for new. There are new entry-level DSLR's hitting the market every year or so. If you are just starting out, buying a used DSLR will let you see if you like photography, and can serve as a good back up to the new model you may buy down the road.