Can you choose to use a starting weapon for a character or do all the weapons have to come from the armory?

you still use your starting weapon. you just cant sell it in the app. after you have purchased from the armory. you can equip to your character with the following restrictions

2 weapons

1 armour

3 equipment

The starting weapons are shown in the inventory, IIRC.

A hero can take up to two weapons to a mission, so you can take (one of your) starting weapon even if you get a new weapon.

You usually don't have enough credits to upgrade all heroes.