My main imaging camera is a Nikon D7000 DSLR
It's an ok, weather proof camera that works nicelly.
News!!
Just Modified my DSLR by removing the IR blocking filter. Very nerv wrecking and the first result was a bit scary, but all worked out in the end.
DSLR - Digital Single Lens Reflex
The most common of all non-compact cameras.
Typically built on a CMOS image sensor. Colour version normally, since the cameras are made for use in normal life.
They can be used in pretty much every astrophotography application. Almost. In some cases, the form factor makes them a bit too big, but for most cases this is the best go-get-started camera.
Here there are many different types of makes and brands. The most common ones are Canon and Nikon. Filters and T-adaptors for telescope fittings are commonly available.
Canon seems to have got most support by the astrophotography crowd. They do make a version modified for astrophotography by removing the IR-filter. This can be done on any camera aftermarket however. Some do this at home. There are instructions out there. Good luck.
Camera control
Some DSLR can be controlled over USB interface from a computer runing software for this.
Almost all has a shutter port by which a simple trigger signal can be sent from the mount, a computer or a hand control.
Intervalometer
Another option is with an intervalometer. This is a hand control with enough intelligence to set things like exposure times, time interval between exposures, number of exposures etc. Some can also do adjustments to ISO setting and more.
Some are just a button with a lock so it can be set to constant exposure while pressed.
Some require batteries for electronics, some are wired and some are IR.