Help painting new chess set

I recently acquired a handcrafted wooden chess set, very stylish & modern but not yet painted. I have no experience in this area, so how do I make them look like my Staunton chess set... Is auto paint okay? Do I need to use a primer first? I want them looking kind of shiny to fit the modern design so should I finish with some kind of varnish/lacquer as well?

Thanks

What types of wood are they?  You could just buff and polish it if you like the colors but just want it shiny. Or you could use wood stain on them.  For example a dark ebony wood stain could be used for the dark pieces or pretty much any 2 stain colors you like. I would suggest looking on YouTube for wood staining tips.

Yes, they all look the same type of wood, the pieces are almost identical except the bases are carved square for one side. The color is similar to the white pieces here: https://cdn.shopify.com/s/files/1/0946/3648/products/IMG_1257_1024x1024.jpg?v=1438624711

I'll look into wood staining, I was not aware of that process so I couldn't find anything when I was searching.

Go with the Rit Dye option. Many more color options. Use polyurethane or tung oil for the finish.