This is another vote for going all-in on First Order. They'll get you BB-8, which leads to JTR. They don't need legendary toons to be good, unlike Empire. A properly built FO team does significant damage in all three raids. Teams like Phoenix are important, but in your case I think they can wait until you're a little more established.... Get strong arena and fleet squads (based on FO and Empire toons you already have), get your scoundrels up and running so you can do credit heists, and then worry about your next goals.
To answer your original question, teams need to deal out damage, absorb damage, and heal themselves, but faction synergy determines how they go about this. Healers are fairly uncommon in this game because toon abilities often allow them to heal themselves; look at KRU's "Focused Rage" or his zeta leader ability. Healers will help you in Galactic War until you get a couple of strong squads built, but then they become fairly unnecessary. The F2P meta Empire team (Palp, Vader, Thrawn, TFP, and Tarkin) doesn't have a tank because they rely on speed, stun, and a lot of damage output to neutralize the other team. Phoenix comparatively does pretty low damage, but they constantly regenerate health and protection so they can slowly chip away at their opponents.
You said you're almost level 65 and want to help your guild...for TW? Your toons must be 6000 GP to enter. Best way to accomplish this is to pick the squad you want and put all your resources into developing them.