There are many variables for buying a camera at the bottom of the pile is the compact, then the bridge camera, then the DSLR.
I have been shooting since 2002, I started with a bridge camera...
you will outgrow compacts and a bridge camera as your eye and creativity change.
But....
The biggest factor that decides is budget followed by photography genre, there are many different styles from: Wildlife and landscape to people and machinery.
The compacts and bridge cameras, will struggle to focus on birds in flight and moving cars etc...
So the most important thing to do is work out a budget, then think about the following kit to add to the camera...
A bag ( back pack type is best)
Decent memory cards ( I use
www.mymemory.co.uk) Spend a bit more and get one of the decent Sandisk Extreme or Lexar Pro cards, lifetime warranty etc and will save the images faster and will transfer them to your computer faster.
A memory card reader- much better that a cable to your camera and faster too... Also means you are not wasting the camera's battery... I pulled my camera to the floor a couple of tmes before I got the reader...
lens cloths (Jessops large blue ones are pretty good @ £5each) lens cleaning fluid...
Other lenses.. now this is something to think about seriously as the glass in the lens is your biggest and best investment. Worth spending the money on what is known as fast glass- ie. lenses with a constant wide open aperture of F2.8 or in the case of some 50 and 80mm lenses F1.4 this means more light can enter your camera....
A good sturdy tripod ( doon't be tempted to skrimp on this as it needs to be solid for slower shutter speeds or longe exp-osure photos)
Adding a flashgun.... There are cheaper alternatives to be had like the Yongnuo flashes from ebay two of those for the coast of a Jessops flash, then you can add radio triggers, umbrellas etc...
Then there are the studio type flashes, but that is for another day...
There is a new DSLR coming from Nikon the D7000 which is 16 mega pixels and should be good at higher ISOs.. If you have the money have a look at the D300s.
I am self taught, but it may be worth you signing up to a course at your local college..
Courses like this one might be a good starting point as you will then see things differently...
http://www.bca.ac.uk/courses/pt/photography.htm
If you want some ideas here is my Flickr page...
http://www.flickr.com/photos/sounds-and-images/