Which nikkor lens will be best for nikon d5100 dslr camera?

Which nikkor lens will be best for nikon d5100 for all purposes?

The "best" lens will be one that's "best" for specific tasks; telephotos for sports/wildlife, wide angles for landscapes, macro lenses for closeups, etc.

The super-zoom "all purpose" lenses aren't "bad," but they aren't nearly as good as special-purpose lenses. They're compromises. They're OK, but give up wide maximum aperture, sharpness, and usually chromatic aberration ("false color" fringing) to give you that wide focal length range.

So what's "best" depends on what you want to take photos of…

It depends on what you're interested in photographing. For now, just get the 18-55VR kit lens.

I have no clue!

The best all purpose lens would be the Nikkor AF-S 18-200mm VR lens

It could be worthwhile to get the body plus an 18-105mm VR. That will have fewer lens changes than the 18-55mm VR, and the 18-105mm is reputed to have good, consistent image sharpness. It will also be easier to work with polarizers, because the front element of the 18-105mm does not rotate to focus. Another, more expensive choice is the 16-85mm VR. The convenience of the 18-200mm VR II is attractive, and it is reputed to be the best of the 18-200mm's, but compromises in quality could still be noticeable at 16 MP.

Nikon's 24-70 f2.8