I would go for all dwarf if pressed for a race. All one class might be a tougher call.... can't say for sure what I would want.
I think a better variant idea to this would be a more general theme.
Like an all nature theme... only druids, rangers, and scouts with nature type races like elves, dryads, etc.
Or mountaineering group... only Dwarves, Gnomes, Goliaths with mostly warrior classes.
Barbarian Tribe group... All characters have function in tribe (Druids, Rangers, Barbarians, Shaman)
Or all Arcane ... Mages, Warmages, Sorcerers, etc in a group. Like a mage guild on a mission.
The themed groups can be very effective in their niche, while creating interesting RP when out of their typical environment.