I was having some problems with textures/meshes not displaying after having the game running for a bit so I verified the steam cache. Now, it crashes on startup right after the logo screen (when it gets to the main menu). What files, exactly, does it check/replace?

It will check and replace any file that came with the game.

Have you changed Ugrids before? the verify could have set your INI files back to default ..any changes you had are gone.
Run any mods?