The player isn't getting to select weapons due to not being the group leader.
To get the group to show up, the player needs to be part of the group before the mission starts (ie. grouped with the blue lines).
I think it's a bit of a catch 22... unless someone can come up with some sort of cunning work around, it's one or the other I'm afraid.
You could have an ammo crate near the player on mission start, or some other way of choosing weapons...