Many different colors needed - How to buy?

I'm a big fan of using model paint, like you'd go buy for, well, models or your Warhammer stuff.

Small bottles, literally any color you could ever possibly want, and it's easy to work with because it's designed to be used on tiny little plastic things anyway.

I've used spray paint in the past, on PLA prints, and it turned out fine.

But I've not researched the topic. Might be that I got lucky :)

Nah you're fine. People use PLA prints for Warhammer terrain and paint them like anything else - spray primer and acrylics, usually, but oils can get you really cool results if you've got more patience.

For tokens, just spray paint is fine. But you'll want some clear coat to seal it, so the paint doesn't chip off while they're being handled a bunch.

I actually have a good amount of experience with this exact type of thing.

Fanciest, nicest, easiest, most expensive method will be to buy filament in desired colors.

Slightly cheaper option, print them all in one color (preferably white), get cans of spray paint in whatever colors you need plus a clear topcoat (I'd recommend matte or satin for game pieces), paint and top coat them

Cheapest option, get one can of white spray paint and a variety pack of cheapo craft acrylic paint (you can probably find a 10 pack for $5), base coat white, use a sponge brush with the acrylic paint (you'll need a few layers), then finish with top coat. Most time consuming and outcome will depend on how many layers you feel like doing.

If I didn't already have a rainbow of different filament colors for this exact scenario, I would go with the third option. You can layer them up until you're satisfied with the quality, and white base coat is always good to have.