All sorts! Pretty much anything you want. The mountainous bits of the UK have sedimentary rocks (shales, limestone, sandstone, mudstone), igneous rocks (granite and ancient volcanic rocks from millions of years ago) and metamorphic rocks (slate, gneiss). Plus tons of other rocks I've forgotten.
Mountains tend to have long and complex histories. For instance Snowdonia in Wales has rocks dating as far back as the pre-Cambrian, and as recent as the Tertiary and pretty much everything in between.
If they are carving caverns, a soft rock like limestone or many sandstones is less hard work than a hard rock like granite. On the other hand, unless they have a good pumping system perhaps they don't want a porous rock, like those limestones and sandstones, or they'll be flooded at regular intervals!
They could even make a home in a salt mine like this Polish salt mine with chapels.
Up to you. Decide what sort of rock your dwarves want to be selling. Slate for roof tiles? Salt? Diamonds? Then have them set up some in that bit of the mountain.