The most expensive but best insulating process is closed cell spray foam. For a large space, with ten foot ceilings it might be no more costly than board insulation. XPS is more labour intensive. For NYC, I'd use t&g 4'x8' x1" boards; if you can't find those, then use 2'x8'x1" t&g. Seal all the joints with building tape--Tuck and Tyvek and two popular brands. I've not used sealers, but a building writer whose information I've always found to be sound, swears by Drylok. (I assume this is not a rubble or brick foundation.) The advantage of steel framing is it's neater to put up (no sawdust) and there are no subsequent nail or screw pops. However, as it's sensitive to moisture, I'd have the baseplate resting on strips of XPS not only to create a thermal break but to keep it away from any minor floods that may occur. Since one inch of XPS is R 5, I always add high density fg batts, adding another R 15. No vapour barrier is necessary, though if this is a permit job, the inspector may insist on one. It wont' hurt anything. (See Building Science links in my first post.) After two years, a number of tiles cracked at pressure points on a brand new home I built. And that's with the tile on top of at least 10" of reinforced concrete and power tamped gravel. Since then, I figure it's a lot cheaper in the long run to use an uncoupling substrate such as Ditra. (If you dont', be sure to keep a lot of extra tiles just in case.) Ditra and cement add maybe 3/8" extra to the flooring height. NYC labour. My condolences!

It won't get out. I've been researching redoing my tub surround and it appears that most people use 15 pound tar paper. I think the tar paper will eventually let the moisture through if any does get in, and it will be at a slow enough rate that it doesn't hurt anything. The only place they seem to use poly is if it is a outside wall and the concern there is you don't want moisture to penetrate from the outside. I'm no expert, but that's the way I read things right now.

Thank you! This is an existing bath/shower enclosure. The sheetrock is already there. The old walls had tile with like an inch of mud underneath. Our GC is putting the hardibacker over the sheet rock to bring the depth back up for thinset and tile which will have a similar profile as the old tile in that there are 1/2" bead trim pieces for the edges...it will not bump the shower beyond the rest of the wall at all. Given this, is it okay to have the following... sheetrock 15lb felt hardibacker 500 thinset and tile Thanks again!

If you buy faced insulation the kraft backing should go firmly against the conditioned side. On the other hand you could use the unfaced type there like the previous poster said. Either way you will still see the insulation from below. If you don't do this it may, or may not, come back to bite you one day.