You're actually thinking backwards about the rivers and mountains – rivers start in the mountains and their flow is dictated by the height of the land, so even though it's absolutely possible to build mountain ranges around rivers, it tends to look more natural if it's drawn in the same order as nature does it. And forests grow where the land is watered by rivers, so they would be added last, to not end up with a forest in the middle of a desert.

That said, your map looks good! Interesting land shape and nice colors.