Kind of easy right now as only been using the 35 and 85 lol
On my D600 my most used lens was a the Tamron 28-75 but it seems these days I don't have as quite a steady hand so maybe something with VR or VC should be what I am looking at.
Looks like most my shots are f2.8-f8 range
If I were you I would consider one of the following before spending too much money
1. Check if the camera needs back/front focusing tuning - You may use free Dot tune and it takes max 30 min for each zoom lens and less for primes. At least you'd know if your camera needs any tuning on certain lenses. Some of your lenses might be fine
2. Narrow down your choices to walk around and general purpose zoom covering 24-85/120 mm focal length and pick one of the following
a. Nikon 25-85 VR - It is a very sharp lens. I have one and used extensively on D600 and D610 and it performs like a champ. This has VR and covers a good range. It does not have 2.8, but only you can tell if you'd need 2.8.
b. Tamron 24-70 F2.8 - Perhaps the most value and performance lens and sits nicely between the Nikon 24-85 and Nikon 24-70 2.8. It has 2.8 which can be very handy, has VC and professionally made. It is sharp, but only downside is you may have to go through a few copies to get one that is top quality. Of course you can fine tune.
c. Nikon 24-70 - No doubt this is the best lens you can buy for this range. The micro contrast, 2.8 and sharpness is legendary and will beat the other lenses on IQ any day. Downsides - bit heavy, pricey and no VR.
d. Nikon 24-120 F4 VR - Cnstant F4, VR and flexibility over others in this group in terms of range. These are being sold under £400 nowadays from panamoz D750 kits and are good value.
Lot of people who use this focal range a lot has either settled with the Tamron or Nikon 2.8 after some time and it might be a good idea to get one and forget about this subject and keep shooting. On the other hand, if you'd wish to try out something, I'd suggest the 24-85
second hand or sold as spare from a kit as it is less expensive to try.
3. For shooting movement with the primes you have (35 and 85), you may need to improve your technique as these lenses are not fast focusing, but using the correct AF setting, fast speed and burst you may get the picture you want. So. you may try that before dismissing the prime.
Here's a
link to my 24-85 VR gallery with few shots taken with on D600/D610 and and I am sure it'd be similar on a D750 (I am getting one). Adding two out of those images here.
1. Wide open at 80 mm and used as a portrait.

24-85 VR by
Anirban Acharya, on Flickr
2. Used inside the cathedral of Cordoba in low light and handheld with VR

Holy Cathedral of Córdoba by
Anirban Acharya, on Flickr