I have a Nikon D5100 and was wondering something?

The lens it has now is a 18-55mm and i was wanting to get it up to 300mm or 400mm so i can take pictures of fast movinf animals and people. So my question is, should i but a teleconverter or just but another lens that is at 300mm or 400mm? If i should get a teleconverter that would get my camera to 300mm or 400mm which one should i but that's is fairly priced? If i must buy a lens then which lens should i choose? Please no rude comments or put downs?

There's no teleconverter that can extend the reach of your lens that far. And even if there were, it would come at a loss of maximum aperture that would make that lens useless. Teleconverters should only be used with constant f/2.8 or f/4 lenses (or perhaps primes), not with variable aperture zooms.

There's a 55-300mm VR lens, as well as various 70-300mm VR ones. The Sigma 150-500mm also has a good reputation.

For fast moving objects you'd need a fast telephoto lens to obtain sufficient shutter speeds then though (VR doesn't help to freeze motion), so you'd probably have to get one of the really expensive constant f/2.8 ones then except for bright daylight situations.