Any of those lenses will be fairly comparable. They all have their positives and negatives...

I have the Nikkor lens which I picked up as my first zoom in that range to use on film and it is what it is, it's built to a price and that shows. It's not the sharpest at 300mm but (although that also makes it light if you plan to carry it around). Because of the popularity and price you should be able to pick it up more cheaply on the second hand market than the others.

Without the AF motor in the D5100 I suspect you're going to get fed up with manual focus sooner rather than later. Ideally you'll want one with a motor built in like the Nikon AF-S version. And without VR or the equivalent, none of them will be stellar without good light.

A lot of the reviews of all the lenses report softness, which will be partially down to the users not adjusting their shutter speed to reflect increased travel (1/focal length is often a good rule of thumb).

A quick poll of reviews on DPReview of the Tamron and the Sigma seem to concentrate on the AF being slow, which it is on the longer lenses anyway. Both the Tamron & Sigma reviews note purple fringing at long lengths, which is every bit as bad as the reported softness of the Nikon. The Tamron has the closest macro focus range of all three and the sigma lenses seem to be pulling in the best user ratings.