I've never hunted coyotes before, but I got a call from my uncle saying there are a ton of them on his property and I should try to get some.

I've already got a .22-250 set up for groundhogs and a spot light, what else do I need? I've heard a bit about callers, are they worth the price? Any suggestions for one? If I'm doing calling sets, how far should I move between sets?

Also, when hunting in the dark, how often should you shine your light to see if they are around? Can I use white light, or do I need a red filter on it?

Thanks in advance.

If you're going to hunt at night, probably will need a partner to shine the light for ya. A red lense is best, BUT you can probably get away with the white as long as you don't shine directly on them, keep the eyes in the hallow of the light. Shine constantly, scanning from side to side looking for the glow of the eyes.
You can find some pretty good prices on used e-callers. How much you spend should be dictated on what you can afford and how much you will use it. I wouldn't spend $300. on a call that is only going to get used a couple times each winter, instead I'd buy a few hand calls and try my luck with them.
Several factors come into play when you're trying to decide how far between stands. Such as wind, terrain, coyote density, call volume, etc. Stay on each stand for at least 15 minutes and only move as far as you think the sound from your call traveled, and make another stand.