General colour choice
Most lighting consoles come with these 12 colors in this order: Red, Orange, Yellow, Lime, Green, Mint, Cyan, Azure Blue, Purple, Magenta, Pink, plus white.
How many colors you plan to use for a look? Typically a lighting designer will want to keep it down to two or three plus white.
If two, any two colours.
If three, could do three right next to each other, you could do every third colour in that list, you could choose a sequence of every other, or you could just choose any three. There are no rules for which colours look best when mixed in lighting, experiment!
Laser/Lighting Designer approaches
If you’re doing concerts, DJs, etc and they are somewhat on the fly, you’re going to want a workbox that has very generically useful things at your disposal. You also don’t really want to be throwing everything at the wall at once either, so you will often pear a song down to two to three colors at most.
If you’re sitting down and really programming something very specific that’s where you might wanna get more into specific hues and saturations and coming up with a maybe a larger color palette for each scene.