It doesn't make economic sense to pay for the triples at this time. An insulation system is only as good as its continuity, it would be like the Hoover Dam having sections only a foot thick.
The attic is usually the best place to start insulating:
Insulation Fact Sheet
I've heard up to 30% of heat loss is through the basement. Concrete is a good absorber and it is surrounded by four feet of frozen ground:
Insulate Basement Rim Joists | thefamilyhandyman.com | DIY Projects | Reader's Digest
If you want to do insulating yourself:
Tiger Foam | DIY Spray Foam Insulation Kits
From a simple engineering perspective:
-Casements hang so the end is exposed to soaking up rain. The box relies on one side of vertical hinges attempting to keep their elongated shape box-shaped against gravity somehow. I've also experienced they tend to be caught by side air gusts and break off, considering the closer is usually a single one at the bottom of the rectangle.
-Awnings are a more stable design gravity-wise, but also can soak up rain at the ends, are nontraditional, and they still feel "closed" even when they're open.
-An inward-opening Hopper seems like it would be self-draining, and easier to clean the outside, but are also nontraditional, and would be a bumping hazard in a tight space.
-Double-hung are traditional, but can have snow/water build up on the top edge, have the line through them, and can bind and be difficult to lock.
I'd consider whatever is architecturally needed first.