Digital Single Lens Reflex. The digital equivalent of the SLR (i.e. no "D" prefix).
Single Lens Reflex means that you see the image via the lens (reflected to the viewfinder via a couple of mirrors) rather than having a separate viewfinder. The once you press the shutter release the mirror flicks up and the image hits the film (or, in the case of digital, the sensor).
http://en.wikipedia.org/wiki/Single-lens_reflex_camera
As for recommends... I have a decent DSLR but I have a hankering for one of these:
http://www.johnlewis.com/230508998/Product.aspx. Quite a fast wide-angle lens but no viewfinder so you're wholly reliant on the display (unless you spend a packet on the add-on viewfinder).
Final thought... think beyond what is a good camera. Think what is a good lens. I don't mean in terms of make/model etc but more from the point of view of spec, in particular speed. Your budget will buy you a camera with a "kit" lens but the lenses are usually quite slow, requiring the use of flash or other method of supplementary lighting, or a tripod is another option if your subject is still enough for a long-exposure (but then you can start to run in to depth-of-field restrictions). Consider buying a body only and the lens of your choice. My 30mm f1.4 is the lens that is on my camera most of the time, leaving my 28-105 in the kit bag because it's f3.5 to f4.5.
No amount of programs and options can make up for the flexibility of a fast lens and, in the case of compact cameras, the ability to manually override speed and aperture (or just aperture at the very least).