[...] And, maybe, if the soldiers had their own equipment always with them, could they be transfered with it [...] In the original UFO it was not possible but maybe this rewrite could it be better than the original.
as far as i have seen, ufo:ai is mostly based on xcom:apocalypse which you can download for free, i think it was on
www.abandonia.com, and that version of xcom not only has the equipment system you requested, but also has more, like the option to play real-time in missions.
xcom:apoc equipment system still made you search for some piece of equipment on a soldier that was not currently in use, and it was a somewhat tedious gui as far as my opinion goes (much better than xcom:eu, though).
luckily we don't have armor in 5 pieces in ufo:ai, and we can right-click! how could that have happened?
assuming there will be some way to defend the base, i think the current system is ok, i mean the system that you equip soldiers when you assign them to dropship, and equips is removed otherwise.
but i would like soldiers to remember what equips they had last time and automatically try to equip when i assign them to dropship.
and maybe the template things are going to help us.
as for the shopping problems, maybe a soldier could be asked to stay equipped even while not assigned to dropship, like being assigned to base quard, or to guard the door to your office (equipped items would not appear in storage and 'for sale').
so, a soldier would need to remember what items he will want to take when he needs to get equipped, and whether he needs to unequip when removed from dropship.