Painting wooden shapes and figures with or for children
Artists-grade paints are often not suitable for children to use or paint toys with because of the pigment density and minerals used. You should look for paints that are child safe - that's not quite as obvious as it sounds, as you're just as likely to find them in the room paints at a DIY store as in a paint box (look for things that are toy safe or EN71-3:2019 certified)
You can use acrylic, gouache or even watercolour to paint wood shapes, but the more watery the paint, the more it will raise (slightly roughen) the wood grain. For youngsters, even felt pen is effective but it will bleed into the wood grain.
There's a company called Tiny Land that make food grade paints for little ones - if you are looking for bright colours for stains, they'd be a great place to look. Primo Craft have a range of compliant paints, and Outlines Art Materials have some acrylics. Earthborn's paint range is compliant and you can buy tester pots to use.
The sealer is important too - again, look for toy-safe, ‘low VOC’ sealers. If you use a children's paint many are designed to be soluble (i.e. washable) so it might be worth doing a test figure before sealing, or you may find you are re-hydrating your paint and dragging it off again, but a stain with a sealer looks really lovely. Different sealers suit different paints.