I'm designing a children's toy and I need it to have a non toxic, water resistant finish that can withstand being put in mouths, being thrown around and that is easy to clean.
Although there continues to be disagreement on this point online (which I expect won't ever stop) any common finish should actually be acceptable for this. The finish needs to be fully cured, see the previous Question What is the difference between "curing" and "drying"? for more on what that means.
Notwithstanding the info below, if you needed to be covered legally I think you'd need to use a finish that's certified safe for this application, or for food-related items. This is not to say that only certified things are safe, but they're the only ones where you can point to a document to show it has been tested and passed for one or other of the applications.
In support of the opening statement Bob Flexner, writing way back in 1992, had this to say:
Safety for food or mouth contact—Some manufacturers market their "oil" finishes as food-safe, but none have FDA approval. In fact, within each of the four types of "oil" finishes, the ingredients (all approved by the FDA) and the formulations are almost identical. It's most likely that all commonly available "oil" finishes are safe for food utensils once the solvents have evaporated and the finish has cured.
More recently, in his published books, he gives almost all finishes an unambiguous thumbsup. In Flexner on Finishing, in the section titled The Folly of Food-safe Finishes, he says the following:
Food safety is a non-issue because there's no evidence of a problem and there never has been. So far as we know, all finishes are safe to eat off of, and safe for children to chew on, once the finish has fully cured (the rule of thumb being 30 days).
I want to make clear that I'm not saying that all finishes are food safe—we can't be absolutely sure about the safety of any curing finish. I'm saying that there is no evidence of any common wood finish being unsafe for food or mouth contact once it has fully cured, so a distinction between food-safe and non-food-safe is speculative.
Accepting the above
If you need a tough coating for the wood (what's called a film finish because it forms an actual film on the surface) then polyurethane varnish is an excellent choice. It is highly resistant to scratches, not so hard that it is brittle and therefore prone to easily flaking off (note however that all finishes become more brittle with age) and highly water-resistant. In addition it is inexpensive and easily obtained which may be important practical considerations on your end.
If you want the wood to have some protection but not have a film on the surface then a penetrating finish is the thing to use. This is exactly what the name suggests, a finish that penetrates into the wood. Possibly the best choice here is what's sold as "Danish oil".
Using varnish you can achieve a high-gloss result on any wood, as well as something more matt if desired. With "Danish oil" the maximum surface gloss will be from semi-matt to satin/semi-gloss depending on a few factors, including the wood used and how finely it is sanded.
Don't want to take the chance
You can leave the wood bare if the species chosen is tough enough on its own. One or two softwoods are and many hardwoods would be. Wood is quite a resilient material and even with nothing to protect it it can hold up surprisingly well.
If you want to add something to the wood so that it looks more finished, something now commonly done with wooden chopping boards, then you can oil it with liquid paraffin (US: mineral oil). Do note this would be 99% for aesthetics, you won't gain any other benefit worth noting.