Long distance wildlife capable lenses require either a heavy tripod or good optical stabilization built into the lenses and not in the camera. Two companies producing these lenses in a range of prices and focal lengths are Nikon and Canon.
I have use both professionally and they are very comparable in capabilities. Nikon cameras are more weatherproof than Canons and have more reliable autofocus. From 2004-2008 pro users switched primarily from Nikon to Canon to get better low light image quality. From 2008 to 2011 the reverse took place with Canon shooters wanting better (more reliable) autofocus performance.
An excellent camera is the Nikon D5200 which also has video capabilities. For wildlife the least expensive lens I would recommend is the Nikon 70-300mm f5.6 VR lens. A good lenses for everything else is the Nikon 16-85mm f5.6 VR. The kit cameras include a lens that will be OK but you are likely to be happier buying the camera only from a place like BHphotovideo or Adorama and then buying the lenses one by one.