I see no reason why that lens wouldn't work just fine on the D7100. A brighter lens isn't
necessary as the D7100 should meter just fine with the lens, and it's high ISO performance should be head and shoulders above the D50, so if you need to shoot in low light it will be a better performer with the same lens. I've always been of the belief that a "better lens" is only necessary after you specifically identify shortcomings with your current equipment.
People have criticized me for using my 24-85mm kit lens on my D800, using all sorts of ridiculous automobile analogies. But the truth is I don't feel the photos taken with that pairing are want of anything, or could be improved if I happened to have a 24-70mm f2.8 on it. Certainly there are specific aspects of certain types of photos that would be improved with that lens, but as a percentage of my total shots I can't possibly justify the cost of the "holy trinity" lens. In fact, I opted instead for a 24-120mm f4 because it bought me reach that I didn't have, something I'd lose with the 24-70mm.
I suspect the only "fine tuning" your lens might need has to do with focus tuning, which you should probably do with all lenses anyway - even the magical ones.