from what I see, once you unlock your racer and complete courses through Grand Prix; if you aim for the food items it will automatically unlock that specific skin.
Once you do a new Grand Prix, you can pick any skin as the default skin for that. For Free Roam, you have a option in menu to easily change what character you want to go about with while doing whatever you want in the open world.
It’s really easy to switch what character and what cart you want.
Favorite course sofar is Bowsers Castle; with Rainbow Road and Boo Cinema right behind.