I've heard only good things about Unity, so that seems like a good default. But it should probably depend on the game genre like DaFranker says.
- Third person adventure - The Blackwell series seems like a good match for this.
- 2D First person adventure - Similar to Phoenix Wright.
- 3D First person adventure - Myst is the first example which comes to mind, but there are probably some more recent ones as well.
- JRPG - just skip the random battles and go straight to the talking.
- Puzzle game - Constantly dedicating most of the screen to the belief network.
- Interactive Fiction - Just text, except for the belief network. Probably with a choice of options rather than an interpreter.
I'm favoring something like Phoenix Wright myself, which means: having a list of locations you can go to. Each location is a static image (possibly looping an animation) which have various points of interest, such as characters to interact with. Interacting with characters will overlay a dialog box. (note: I haven't actually played the game, so this may be slightly off.)
Mostly because it would be easy to do and because we can start with just text and add in the clickable images as we get assets. Also because I dislike the tedium of being forced to walk back and forth between locations in games for no reason which most of the others seem to require to some extent. (Unless the traveling is interesting or unusually beautiful in itself which probably shouldn't be a concern for this game.)
For that... I don't know, it could be that Unity isn't worth having a fairly big framework which we won't use much of.