I went to DxOMark.com and checked out the Nikon 24-85mm f/3.5-4.5 ED VR lens. It gets an overall rating of 22 on a 24.3mp D750, with a sharpness rating of 15 perceived mp, which is fine. You can compare it to the much more expensive 24-70mm f/2.8 , which gets an overall rating of 26, with a sharpness rating of 16 perceived mp. You will probably be happy with the lens.
As far as zooms vs primes, I almost always keep the trinity of a 12-24mm f/2.8 (in my case a Sigma 14-24mm f/2.8), 24-70mm f/2.8, and 70-200mm f/2.8 in my photo backpack along with a 35mm f/1.8m, 50mm f/1.4 and 85mm f/1.8. In general, primes are smaller, lighter, sharper and faster with a shallower DOF at large apertures, which can help separate your subject from a nicely blurred background, but 95% of my non-wildlife shots are taken with the trinity. In fact, I rarely take my Tamron 70-200mm f/2.8 G2 off of my D850. It is nice, however, to be able to call on a prime when you need it. I don't think of primes or zooms as "better" than one or the other, I think of them as tools in my toolkit and pull out the right one for the job at hand.
Since most people take good care of their camera gear, I save some money and buy used when I can. I am happy with
KEH.com for used gear. They have a good rating system so you are pretty sure you know what you are getting when you buy and they have a 14 day return policy. If you are really concerned you might not like the lens, then rent one first. I am happy with lensrental.com when I want to try before I buy. Good luck and I hope you enjoy your D750. It is a great camera.