By the end of ME3 (my PERSONAL assessment):
Kaidan - Sentinel (Biotic/Tech toned)
Ashley - Soldier (Combat/Tech toned)
Liara - Adept (Biotic/Combat toned)
Wrex - Vanguard (Combat/Biotic toned)
Garrus - Infiltrator (Combat/Tech toned)
Tali - Engineer (Tech/Combat toned)
(gets more tricky with many ME2 characters, as Bioware went more with hybridization)
Miranda - Sentinel (Biotic/Tech toned)
Jacob - Vanguard (Combat/Biotic toned)
Mordin - Engineer (Tech/Combat toned)
Jack - Vanguard (Biotic/Combat toned)
Grunt - Soldier (Combat toned)
Samara/Morinth - Adept (Biotic/Combat toned)
Thane - Infiltrator (Biotic/Combat toned)
Legion - Infiltrator (Tech/Combat toned)
Zaeed - Soldier (Combat/Tech toned)
Kasumi - Infiltrator (Tech/Combat toned)
(a little tricky with ME3 characters)
James - Soldier (Combat/Tech toned)
EDI - Engineer (Tech toned) (this one is especially hard, as she has a strong 'infiltration' aspect, but I regard her an Engineer at heart)
Javik - Vanguard (Biotic/Combat toned)
~~~
What may qualify as Combat toned? Weapons beyond pistols/sub-machine guns. Combat abilities that are not elemental or highly technical. Greater focus on weapon, armor stats. Being offensive focused (which is just enough for Mordin, for example).
AKA gun powers and weapons.
What may qualify as Biotic toned? Biotic abilities. Greater focus on powers cooldowns. Being more defensive focused.
AKA biotic powers and manipulations.
What may qualify as Tech toned? Tech abilities. Greater focus on powers improvements. Being more utility focused.
AKA technical powers and elements.
IMO you see Combat above all, because this is Shepard's Story and his is simply more Combat oriented than what we may hypothetically see in future games. We were the soldier, and we needed a good team to at least affirm that.
It is my prediction, or at least hope, that the next game(s) will shift things more to the Biotic side. Still plenty of Combat, but not as necessary as before. Less War for Survival, more Tactical Operations
. And at some point after that, I hope we get a Tech focus (2-4 games from now).
~~~
Soldiers:
-Ashley
-Grunt
-Zaeed
-James
Adepts:
-Liara
-Samara/Morinth
Engineers:
-Tali
-Mordin
-EDI
Vanguards:
-Wrex
-Jacob
-Jack
-Javik
Infiltrators:
-Garrus
-Thane
-Legion
-Kasumi
Sentinels:
-Kaidan
-Miranda
~~~
Toned characters:
Combat:
-Ashley
-Liara (yes really, Warp AMMO in ME3)
-Wrex
-Garrus
-Tali
-Jacob
-Mordin
-Jack
-Grunt
-Samara/Morinth
-Thane
-Legion
-Zaeed
-Kasumi
-James
-Javik
Biotics:
-Kaidan
-Liara
-Wrex
-Miranda
-Jacob
-Jack
-Samara/Morinth
-Thane
-Javik
Tech:
-Kaidan
-Ashley
-Garrus
-Tali
-Miranda
-Mordin
-Legion
-Zaeed
-Kasumi
-James
-Kasumi
*NOTE: I may have weighted things a little too strongly for Tech. If you remove some of my more vague requirements, at least a few on that list may easily be removed (like Ashley and James).