Koi are hardier than platies when it comes to overwintering outside, but they are on par with goldfish in terms of dirtiness (and willingness to eat plants). They need large volumes of water and lots of space as they easily grow over a foot long. Ideally for a koi pond you'd need 500+ gallons of water, but the biggest you can go is best. While koi would be able to stay outside year-round, you are going to end up paying a lot more for this project than a small prefab pond.
Goldfish can also be overwintered outside in most locations (again provided the surface doesn't freeze over and the pond is deep enough). A goldfish pond will be much less expensive than a koi pond as you wouldn't need the large area or massive volumes of water.