A:
The Nikon D3100 with an EH-5a AC Adapter. I know it is somewhat impractical at sporting events. Find a cheap portable AC/12V power battery. In addition, you'll need a really fast memory card like the SanDisk Extreme® Pro™ SDHC™ UHS-1 Card (8, 16 or 32 gig). I have the 8 gig. You'll need a good zoom lens like the AF-S DX NIKKOR 55-300mm f/4.5-5.6G ED VR. It has AutoFocus, Vibration Reduction and really fast motor speed. Flashes are usually not allowed at sporting events so you can skip that.
That would put you just a bit over $1000 but near professional photographer's results. YMMV.
When you turn pro get a hold of an AF-S NIKKOR 200mm f/2G ED VR II.