I would recommend the D5100 out of the three cameras you listed. Having said that, either the Nikon or the Canon would give you fantastic results.
The reason I suggest the Nikon is that they come with considerably better warranty in all fashions. Two year warranty on the body (as opposed to all other manufacturers offering a one year warranty) and five years on all of their lenses (as opposed to one year, again). Also, Nikon ergonomics are renowned and they offer a range of good quality, inexpensive lenses for beginners/families/etc.
In reality though, the cameras are very similar and unless you're a very avid photographer, most of the differences wouldn't be obvious. Both have great photo quality, both have great video quality, and both are built well for the price. People love to nit-pick, and that's what most of the differences and discrepancies on 'review' sites come down to. Neither one of these will make your pictures an Ansel Adams if you don't know how to use it, or you don't know the fundamentals of photography. However, both are easy enough to use that you can just point and shoot and still get good photos. If you do know your photography, both can be used as a tool to take top quality images.
So in the end, it all comes down to you. Go into a camera store and try them out, see how they feel in your hand, see how you like the weight/button placement/fit of the camera, because for most beginners that will make the biggest impact; not one camera having a slightly lower S/N ratio, or 0.1 EV more dynamic range.
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