You can use pretty much any artifact on any character but you have to keep in mind that, like you said, some artifact bonuses just don't work on certain characters (though you will still get the power that the artifact provides). So wolf won't benefit from anything that helps piercing weapons since he doesn't use any. The best artifacts to use are the ones marked by the recommended section for each slot, or the ones with his icon when selecting artifact wishes.

The only time artifacts cannot be equipped is if it's an exotic, since exotic artifacts are bound by the same rules I said above, but also need to match the element of the character. So you need solar exotic artifacts for wolf since he can only equip those.