There aren't any bad DSLR cameras, but some are a bit better than others. There are four manufacturers: Canon, Nikon, Pentax, and Sony. Canon and Nikon are the two most common. Pentax and Sony are often a bit better value, but harder to find in stores. With you budget, you are looking at the entry level mostly, unless you buy an older camera, used, or refurbished.
The D3000 is last year's model, the replacement is the D3100. Same with the D5000; the new model is the D5100. With Canon, the T3i is the current model; the T2i is the older one. Of those, the T2i is probably the best value. Every professional review has been good, ranking it at the top or near the top for its class...you could say it is the Honda Accord of DSLR cameras.
All DSLR's are sold either as a body only or with a "kit" lens. Buy it with the lens because it is cheaper than buying a body and specialized lens separately. The kit lens is almost always a 18-55mm, which is fine for general photography. But for sports, you would want a longer focal length. Usually you can get a two lens kit; the T2i can be had with both 18-55mm and 55-250mm lenses (but that would be approximately $1000).
Canon T2i review: http://www.dpreview.com/reviews/canoneos550d/
If you want a body and two lenses for $700, a best buy would be the Pentax K-x with 18-55mm and 55-300mm lenses: http://www.buydig.com/shop/product.aspx?sku=PKKXKT255300K
Pentax K-x review: http://www.dpreview.com/reviews/pentaxkx/
I posted before about finding a point and shoot would take great action shots and pictures.