Or should I spray something like a white primer on first before spraying with Zandri Dust?

Absolutely. GW and Army Painter (to name a couple) make those sprays so you can more efficiently basecoat your models. If you're planning on, for instance, doing your Rebel Troopers in a desert colour scheme, this will allow you to skip the step of spraying it white, then painting Zandri Dust over all the clothes.

Do it this way, and you just need to pick out the faces, guns, and other little details. Way faster.

None of the GW sprays are proper primers, but I use them, too, and never had an issue with just spraying them on the model. If you want a proper colour primer go with Army Painter, their sprays are more difficult to use, though. Never had a problem myself, but I know a friend butchered a whole bunch of models by not following the instructions exactly enough. Since Army Painter spray is a proper primer, they were a pain to strip clean.

I’ve always read that one could use a regular spray can color in place of a proper primer, but I’ve never done this myself. Primer gives more “stick”, so subsequent base costs work better on it.

You can of course but you should know the GW colored sprays paints are not actually primers unlike the AP ones. I'd recommend you give them a quick gray primer coat first.

I Highly recommend primering black or gray first as well, especially on the underside of the model. Then hit with the Zandri so you don't have to over-coat.

Make sure to wash (yes with water) your models first though.

Most molding techniques leave some sort of releasing agent residue that can screw with your base-coats if you don't rinse it off first.

So give your troops a shower.

I always wash metal or resin models, but honestly I rarely bother with hips or abs plastic. Do we actually know what material these are made of, and whether they need to/should be washed for a release agent?