You don't collect the new coin pokemon, just the coin, but you need 1 coinmon to find the others, after 100 coins you unlock the 'true' coinmon. They are everywhere, you get the first one pretty early, you can get them all once you unlock all the travel modes from the legendary.
The chest is not a mon, is an item, you fill it with coins and give it to one coinmon once it's filled it evolves.