How do I figure out which rear-exit stoves will work for me?

New house, new stove puzzles. In one room, there's an existing open-hearth masonry fireplace that I'd like to re-purpose to host a free-standing wood stove just in front of it. I'm aware this will require using a rear-exit flue woodstove. My question is how do I know from the specs of the stove if it'll work in my application or not? What do I measure on the existing hearth? What other measurements/offsets/whatever do I need to consider?

We're not moved in yet and the only picture I have of the room was from the floor refinishing, so the fireplace is small in the frame but it should give you guys an idea of what I'm working with.

Thanks as always.