[X] mle.1927 Hotchkiss 13.2mm
Drums tend to be a little unreliable even when they're not mounted to a mech and difficult to swap out.
[X] 58mm Crapoulliet mortar
Proper tanks tend to like big cannons, shooting stuff at high velocity, but mechs really won't - when stability matters, minimizing recoil is important, which means big HE projectiles moving slowly.
I do want something punchy as well, which rules out the mountain gun. Either kind of rocket would be okay... except for the inability to reload. Running back to resupply every time you get in a fight seems bad, and mounting enough rocket tubes to counteract both that and limited accuracy seems heavy.
Edit: Removed one vote since this is not approval voting. Sorry, I forget sometimes which quests use it and which don't.