Shamu,
350 gallons is not big enough for koi. I'm guessing that the pond isn't over 24 inches deep, so koi wouldn't really have a lot of room to move around, and they get big fast! Koi keepers typically build six to eight foot deep ponds for their koi and they have no plants, and massive filtration. It isn't uncommon to see ponds bigger than swimming pools, stocked with just ten or twelve koi....... Ideally, koi should have about 1000 gallons per fish to accomodate their potential growth.
I've had wonderful luck with shubunkins and comets in my 2000 gallon planted pond. They get along really well, but don't seem to tolerate fancy tailed varieties. Every fancy goldfish I've put in with them has died, so I'm just sticking to the shubbies and comets for now.... You might want to stock all fancy varieties or all commons..... In the winter there you might have to consider bringing in fancy goldfish, but commons and shubbies would probably do fine with a de-icer
As for winter care, a bubbler will work, but IMO a de-icer is better. A bubbler brings the warmer water from the bottom of the pond (where the fish hang out in the winter) to the top of the pond. It can super cool the water which is not good. Also, a bubbler can freeze over and you'd have to go out and gently break the ice dome over it.... A de-icer just floats at the top of the pond and keeps a hole open in the ice. You just plug it in and it works and the water stays still, providing layers for the fish to stay in... Buy a metal cage for it, to keep it from touching the sides of your pond.
I think you'd be happy with the 350 gallon pond if the price is about the same as the 150. The larger the pond, the easier it is to balance it out and the less chance for water quality issues. And the more fish you can have, of course!

I'm very excited for you. You'll really enjoy a pond of your own.