Also see what kind your close friends have as well. A lot of my friends have Canon cameras and I chose my first Canon Digital Rebel based on the egronomics and features as well as many of my friends having the same camera. It also helped that we shared lenses and I was able to upgrade my lenses by buying used ones from a Canon pro friend.
In addition to trying the ones in the store, be sure to hit up your friends to try out their DSLR. Most of the ones in the store either have no lens, or are in poor condition, I find them useless as a demo. All they are good for are to see if it fits right in your hand.
As far as the differences between in-body stabilization vs. lense stabilization, you can google for reviews on that. The biggest difference are when you start getting lenses over 200+mm..that's where lense stabilization has a distinct advantage. For shooting outdoor sports, anything in the 70-200 f/4 range is suitable. Indoor sports, you'll need something like a 70-200 f/2.8 (this is where things get pricey). No matter which manufacturer you pick, a 70-200 f/2.8 lens will run you $1200-$1800.
Something new to consider is also HD Video. It's the latest rage among DSLR's so you might want to consider a DSLR that has HD Video as well. Canon's new T2i and Nikon's D5000 both have HD video. (1080p and 720p). Sony, Pentax and Olympus also have DSLR's with video.
The new 4/3rds "Pen" type cameras are also another consideration. Olympus Pen series (E-PL), Sgima DP2, and Sony Alpha Nexx are all new offerings giving you DSLR speed in a smaller package. However, with their limited lens offerings, its not for everyone.
Check out Costco or any other warehouse superstore for pacakge deals as well. YOu can frequently find good Canon and Nikon packages for under $1000 that gives you 2 nice lenses, camera case, and many other useful things for beginners.
Good luck with your search
