I get asked quite a bit about different types of cameras. There's DSLR (digital single lens reflex) and mirrorless DSLR. Most professional photographers use various brands of DSLR cameras such as Nikon, Canon, Olympus, Pentax or Sony to name a few. The traditional DSLR uses an optical viewfinder that a mirror to reflect light from the lens to the viewfinder. This allows you to see exactly what the lens sees, so if the picture is in or out of focus you'll know. You can also track action through the viewfinder, which makes a traditional DSLR camera the best choice for fast action like sports, or in my case combat. DSLR's have a quite focus response time and are known for their ability to shoot multiple frames consecutively, unlike their mirrorless counterparts. The traditional DSLR can varry in prices on average from $400 - $6,000. You can get your hands on kits, which come with a body and lens. You can also see what's out there for certified used and get a great deal! Check HERE from time to time. Just remember that you should be extra cautious if your purchasing anything from E-Bay, Craig's List and the like. You never know what that camera's been through.
On the other hand, the mirrorless DSLR is lighter, more compact and definitely more quite. If you don't the attention drawn to you, this is a great option - not to mention you can fit most of them in your purse or pocket. Without a mirror it uses an electronic viewfinder, which means you have no traditional viewfinder that you put your eye to. Instead, you use an LCD (Liquid Crystal Display) screen on the back of the camera. Most mirrorless cameras use pancake lenses, which don't detach from the body. However, more and more are offering interchangeable lens options. There are a ton of mirrorless DSLR camera options such as the Nikon J1, Nikon V1, Panasonic Lumix, Samsung NX-200, Pentax Q, Sony NEX, Olympus E-P3, Leica M9, and so many more... Phew. These cameras start around $400 and go up to $1,200, with the exception of the Leica which is somewhere in the neighborhood of $6,995'ish.
If you choose to go down the road of a mirrorless DSLR camera, then you have accessory options. There's M. Zuiko Micro 4/3 Lenses for the Olympus, External Flash for the Sony and Colorful Cases for the Nikon.
Both types have their benefits. I have both and use them for various projects. I hope you find one that suits your needs. Happy shooting!