I only have 6 soldiers unlocked at the moment, so I can't say for the 200, 300, 400, and 500 squad point soldiers, but with all of mine so far, as previously said, it all depends on the loadout you have for each soldier... Meaning which Class set has a star next to it when in create a soldier. The class set that has the star is the default loadout when you play with your squad, or if you're offline and a random person challenges your squad. Hope this helps.
Make sure to check that the AI Loadout selection is on the class set that you WANT them to start out with. I have seen sometimes a loadout for one of my soldiers is different from the one I selected. I.E., one soldier I had selected an SMG as a default, but when the game started, he had a sniper rifle. So make sure all the classes are set up for how you would play in online multiplayer. It is the luck of the draw if you will win in Squad assault. If you're more cautious on Strikezone, you may win in by a big margin. If you're cautious when playing on Flooded, Stonehaven, or even Freight, you may not win.