In Zone 5 the basement wall R Value minimum under the International Energy Conservation Code (IECC) 2012 is R15/19. The first number is for continuous insulation.

So your second approach is a bit shyÃÂ of minimum. Using high-density batts, R15" for 3.25" thickness, solves that.

Building Science Corp. recommends the board/fg combo. I have used that a few times. However, Green Energy Advisor writer Martin Holloday is sceptical of fg anywhere in a basement. Instead of FG, you could use rockwool, which is unaffected by moisture.

If space is not a major constraint, thicker EPS (expanded polystyrene) may do the trick for less than XPS.

should we put down a layer of foam like a sill plate gasket under the pt board?

Sill plate gasket is used as an air seal. You want a moisture barrier to prevent rising damp. Six mil poly will work. Better yet, use strips of XPS; it not only inhibits rising moisture but elevates the plates an inch in case there is some temporary minor flooding.

A final consideration. For a faster neater job with guaranteed straight walls, you could use light steel rather than dimensional lumber for framing.

Thank you for your help! The only area that we have a problem with space is right at the bottom of the stairs. That's where they ran the water into the house. lovely planning on their part!

I'll look into rockwool. It sounds like that would be a better choice.

Thank you for your answer to my question about what goes under the plate.

I'll look into metal studs.