DX fixed aperture zoom

I am looking for a zoom lens thats has 60-70mm right in the middle. I work in my home studio and find that about 60-70 is where most of my shots end up being. My big thing is Id like below an f4 aperture if at all possible and Id like it fixed. My budget is $800 absolute max and I have no aversion to third party lenses. Itll be on my d5200 so I really want a foucs motor in the lens.

I was thinking about looking at a used 24-120 f4. Any other suggestions? Cheaper is always better but I still want good quality obviously. I will be upgrading from my kit lenses 18-55 and 55-200.

The Sigma 50-100 fits that fairly well except it's probably a bit over budget.

Trying to stay on budget the Tamron 24-70VC is another option as is the Sigma 50-150/2.8 OS or the Tokina 50-135/2.8

Hope that helps

how about a used 17-55 f 2.8?

55 is way to short

There is an sigma 50-150f 2.8 OS. Used is about $700-800

The best prime lens, irony to my previous belief will be the recently launched Sigma Zoom 50-100/f1.8. It is much sharper than many of the older primes with same aperture and it fits nicely to your budget