In looking at sensor scores on DXO, you will find the Nikon sensors perform better than the Canon, especially at a higher ISO when you will want to bump it up for indoors or sports and using a slower variable aperture lens. To fit your budget, I would suggest something like a Nikon D3200/3300 or 5200. For a longer lens for sports, I would choose the Nikon or Tamron 70-300. You would be using the sharper center of these full frame lenses. On DXO, you can also compare these lenses to the Tamron 16-300 or 18-270.

The Canon t5i is also the 700D
http://www.dxomark.com/Cameras/Comp...S-700D-versus-Canon-EOS-7D___928_870_619