A flowchart for picking a trio:
1. Pick a priest. Having some kind of healing hugely increases your margin for error. Cleric and Shaman are both superb, but Druids got buffed nicely in Velious and have ports.
2. Pick a tank. Monk, Warrior, Paladin, Shadowknight, Bard, and Ranger are all reasonable choices here. Hybrids mix a bit better with shamans because their higher threat means slow lands earlier.
3A. Pick a support class. You need one of Shaman/Enchanter/Bard for slow, haste, mana regen etc, so if you don't have one this is your last chance to fix that.
3B. Pick a DPS class. Otherwise, your primary issue is damage, and reasonable choices there are Enchanter, Necro, Mage, Rogue, Ranger, and Monk.
A few trios suggested by this algorithm:
- Cleric / Monk / Enchanter (the best IMO)
- Shaman / Paladin / Rogue (totally legit)
- Druid / Bard / Mage (unconventional but would work quite well IMO)
- Cleric / Shadowknight / Bard (low DPS, but not terrible)
There are certainly plenty of unconventional trios possible but without a priest and tank they will be based on either fear kiting or pet tanking and so won't be very flexible.