Any of those could be correct, depending what you want to say. Gush means that a lot of water was coming out. One could talk about flooded river gushing out over its banks. Spouted generally means that water shot up in the air. Some geysers spout water like clockwork. Spew usually means that something sprayed out in different directions. People talk about vomiting as spewing. Spurt means a brief gush or spout or spew. When people drink milk and laugh, sometimes milk comes out their nose in little spurts.

Christopher has given you an excellent summary of how we use these verbs - brief but comprehensive. Nothing more to add! I've been following your posts with interest, and I hope that your voyage of exploration into the richness of the English language is proving a source of fascination rather than frustration to you. Unlike French, which has sought to preserve its purity, English has always begged, borrowed and stolen from other tongues and been as inventive and imaginative as possible with the building blocks of language. As you are discovering, we have a vast storehouse of vocabulary, with tens of thousands of words all subtly and delightfully different from one other.