Teh shutter speed has nothing to do with the camera, and everything to do with the lens. With a typical kit lens like the 18-55 or 55-200 and 75-300, your shutter speed is not going to any different than it is on a point n shoot. If you want a faster shutter speed, look at faster lens, like the 50mm f/1.8 which is an excellent lens, super fast, and bargain priced at only $100. The 50mm is only a mild telephoto angle, so its not the best idea for getting close in on your kids sports games. But its a great walkaround and general purpose.

And yeah, I would abandon the D3000 idea in favor of a Nikon D200, Canon 40D, or Sony A700. If you don't feel like overpaying for lens and accessories, stick wtih Canon or Sony and avoid Nikon.