Although it heavily infers it during the tutorial videos, you don't have to match the Divisions to their suggested weapons. It might seem natural that a Division which gives you access to incendiary ammo for shotguns should only be used for loadouts with primary weapons like the trench gun, but that's not necessarily the case.
To get the most out of Divisions you should instead throw away what the game suggests and match them with whatever weapons you want. The ability to sprint father and silence your guns doesn't only have to apply to SMGs, and if you prefer that style of play but love maining weapons like you M1 Garand, there's no reason why you can't match the two up.
Likewise, keep an eye on the other unlocks that come with each Division, as they're often more vital to different playstyles than the base perks. For instance, the ability to carry both a tactical grenade as well as a lethal one can transform the otherwise unappealing Expeditionary class one of the best in the game, and encourage you to take a chance on it.
It's easy to glance at a Division and think it's not for you, but experimenting with different weapon and class combos is the best way to find success in WW2's multiplayer.