XCOM 2 SQUAAAAAADD

[Dane Regan]

Edit: Ignore this. It's for if I used you guys for the Long War mod. Which I won't be doing for a while.
[spoiler]
I made a slight derp and listed the original base game classes. Since I'm initially playing with the Long War 2 mod, there are some changes (top post is now updated):

• Robots and Psionics are unchanged mostly.
  
• Assault - Shotgun people - Clearing out weak groups or taking down big guys. Also get a stun gun. Very mobile. Good for flanking and skirmishing.
  
• Grenadier - Grenade Launcher - Grenades for damage or support (e.g. smoke, flashbang) purposes - Still get a rifle.
  
• Gunner - You shoot people with a big gun. You can also stab people with a knife if they get too close. Damage or field control.
  
• Ranger - Like assaults, are good at surviving. Get a sawed off shotgun with your main gun. Direct accurate damage or generally just shooting everything that comes near you.
  
• Sharpshooter - Sniper Rifle - Hardscope pro or Quickscope people. Some supporting options.
  
• Shinobi - Sword + Shotgun/SMG/Rifle (SMG is lightest so you can move faster) - Inflitrating and stealth (including helping on the campaign for such thing) or assassin sword guy.
  
• Specialist - Flying robo thing + guns - Healing or hacking (anti-robot) or generally assisting the squads damage.
  
• Technical - Heavy weapons in addition to your default gun - Spec for burning everything (crowd control) or lost of explosions (destroy cover and do a lot of damage).
  
• Officer - Is taken with another class, there will only be a few of them though - Help people shoot or help them not get shot.
  

So Trixie would be a Shinobi (swords)
Tearen would probably be a Specialist medic (maybe even Officer as well)
Dante would be Assault because of the skirmishing and damage potential. 
Jak will still be whatever class pops up for him to fill.

Note: When the dlc comes out (in 5 weeks or so), original classes will be relevant again.
[/spoiler]