How much does the thinset add to the hight of the finished floor? I'm trying to match the 3/4" hardwood in the next room as closely as possible. Would it be better to use 1/4" backerboard or 1/2"? The tile itself is 1/4".
You need thinset under your backerboard and thinset under your tile. Typically the thinset will elevate the product about 1/16" depending on how you mix it and how you spread it and what product you choose.
HardieBacker comes in 1/4" and 7/16" even tho they label the thicker product 500 and call it 1/2".
Typical glazed ceramic floor tile is about 5/16" but no guarantees on that, they vary.
I think your safest bet is the 1/4" so as not to arrive at your destination too high. That should work out for you.
Now with that out of the way...is your structure suitable for a tile installation to begin with. There are rules believe it or not.
Depending on the tile I have found it works better to use 5/16" Durock brand backer board for matching up to hardwood.... 1/4" Hardibacker is just a wee bit shy on occasion.
The skinny Durock's what I use, as well. Actually it's made by Durock with Daltile's name on it (Durabacker), but just the same. :-)