Things to look for:

Mount system

The lens has to match your camera for you to be able to attach and use the lens. In your case, a Nikon D750 is in the Nikon F mount dLSR lens system. So you need to look for lenses that are for Nikon F. Nikon does also make a mirrorless system, Nikon Z, and those lenses would not be compatible.

Sensor coverage

You also want to get a lens that covers your sensor with its image circle. While you can get a crop (DX in Nikon terms) lens and use it on a full-frame (FX in Nikon terms) body, the resulting image will be cropped down to crop dimensions, reducing resolution. If you didn't shoot Nikon, you could look up the specific manufacturer designations for full frame or crop on this Q&A:

What do all those cryptic number and letter codes in a lens name mean?

Focal length range

If you want a lens that zooms in and out, you need to look for a lens that has a focal length range, which will be specified as a numerical range in millimeters (e.g., 18-55mm). If the lens only has a single focal length (e.g., 50mm) then it's a prime lens that does not zoom.

Focal length distances

The focal length numbers themselves will tell you how the lens frames and what working distances are most likely to work for you. The shorter the numbers are, the wider the view on the lens will be, and the closer you can get to a subject.

Most vlogging/selfie shooting is done from fairly close (arm's length for shooters holding their camera in their hand), and people typically want to get the context of the space they're in into the shot with a wider field of view, so the most common lenses used for this are ultrawide or even (in the case of action cameras) fisheye lenses. But these can do perspective distortion when used in so close and may also exhibit barrel distortion from being so wide.

If you have more room, want to frame more tightly, or would prefer less distortion, a longer lens might do the trick, something in the wide to short telephoto range favored by portrait shooters.

In general, full-frame equivalent focal lengths boil down like this:

• Ultrawide: under 24mm
• Wide: 24-50mm
• Normal (not wide/not tele): 50mm
• Telephoto >50mm
• Supertelephoto >300mm

Figuring out how that would work with a specific camera depends on the sensor size being used. On a full-frame camera like the D750, you can just go with those equivalent numbers. But on something like an APS-C mirrorless camera, say a Sony a6100, then you'd have to divide that number by the crop factor of the sensor (1.5x), and 24mm would be more like 16mm.

IOW, you probably want something like the Nikon 14-24, but you can probably afford something more like the 28-70 or 24-120.

Minimum focus distance / macro

While shorter focal lengths help you take images with the lens closer to the subject, most lenses for larger-format sensors will also have a minimum focus distance. If the lens is closer than that distance to the subject, it cannot focus.

For extreme closeups with a full-frame sensor, you may need a specialized macro lens. And a "true" macro lens (one that gives you 1:1 magnification, where the size of the image on the sensor is the size of the subject) will always be a prime, and typically be in the normal to short telephoto range in focal length. Most full-frame true macro lenses are around 100mm.

Cinema/video-specific features

Additional cinema features you might want in a lens for video (but that may cost a ton):

• Silent autofocus motor
• Lack of focus breathing (when the lens changes focal length as you change the focus point)
• Focus rig gearing
• Clickless aperture for continuous, rather than stopped adjustment