As far as universals go, these are indispensable:
Battle Hardened
Supply Max Increase
Combat Intuition
Sprinting Grenade
Sprinting Reload
Resupply Rate Increase
Downed Fire and Silent running are useful, but not indispensable.
Medic; Nessicary:
Increase Supplies
Improved Increase Supplies
Improved Life Buff
Self Rez and Laz Nade are very nice to have, especially if you are often medic, but again not indispensable.
Engineer; Nessicary:
Improved Weapon Buff
Extra Landmine
Nerves of Steel
Extra Kevlar and Turret 1,2,3 are nice to have, but putting that many points into engineer makes your jack of all trades a bit lopsided.
Operative is interesting, its basically the only class where there are two playstyles to choose from with skills. There is information gathering, and disrupting the enemy. For a jack of all trades, you are better off to choose one or the other based on your personal preference. I prefer ‘information’ because its more directly useful to the team.
Information Operative:
Homing Beacon
Comms Hack
EMP Grenades
Harrassment Operative:
Sticky Bomb
Caltrop Grenade
EMP Grenade
Hack Turret and Control Turret are interesting skills, and worth taking if you use them. I end up shaving them off for this build simply due to lack of skill points.
Soldier is another hard one to choose for. None of their skills apply to their objectives or teamplay, save Extra Magazine. As such, extra magazine is the only one I would call “Necessary”. To Greatly Increase the soldier usefulness though I would put 4 points into soldier.
Soldier:
Extra magazine
Grenade Mastery
Frag Blast
Grenade Damage
AP ammo, Kevlar vest, and Flashbang OR Satchel Charges (not both, only have 3 active ability slots, and Molotov uses one) are all nice, but not required.
There are 13 Skills in this list that I say are necessary. 16 if you count one of the operative builds. 19 if you take the soldiers three frag skills. For the last skill, i would probably take Self Rez, but I’m partial to playing medic.
If you drop one of the classes though, you are given a lot more leeway in choosing skill for the other three.