On the menu before starting a contract, tab over with
from the Contracts menu to the Loadout menu.
Staying on the Loadout menu, tab over with
from Soldier to Development.
Purchase any skill under any of the 4 categories (mask, suit, support, gadgets). The first tier upgrades for all categories cost 25,000 credits.
None of the first tier unlocks need any contract tokens (skull icon) or challenge tokens (stars). 25,000 credits can easily be earned by looting dead enemies.