One way of tackling unique units is that Arnie Stalone could come along with 'Arnies minigun' which only he can use as well as being very strong and not setting off heat detectors. You can swap out his gun/extra kit if you want, but no one else would be able to use his minigun. This allows his gear to be unique, but allows you to configure your squad.
I don't really think it matters how you do it - just as long as you allow the player to have control over their units. From the sounds of how you're doing things, I'd just give them full control of the load out and allow them to upgrade weapons and kit with their mission gains. Just make it so that any upgrades stay for that item type - so if you upgrade a machine gun to +5 accuracy, all machine guns that you give to your troops will have +5 accuracy.
I see what you mean, but again, the minute you have control over the units' inventory you no longer feel that much compelled looking for new units to hire since you can "build" them yourself. I believe unit uniqueness is not compatible with full arming control.
Another thing I truly want to avoid is making items bound to specific units. I want every unity to be able to use any item at any time. Units' skills are the one factor that will decide how effectively items can be used, if used at all, like some medical equipment. So, Arnie was just killed but you can still pick up his weapon and use it.
I want players to look forward browsing the Hiring Market to see what's new. From a realistic view, all your units are freelancers and they have their own gear and combat preferences so their equipment is what they are proficient with and what they take from one mission to another.
I was thinking yesterday about the loot you gather from missions and I think I will ditch it. You will simply get paid for accomplishing mission objectives. It's easier to balance with less risk of giving too much hi-tech to the player too quickly. This also allows me to craft more diverse and surprising missions.
I don't intent creating a X-Com like game but Rebelstar on steroids