I'd advise against shaman healer also - mostly because of the lack of AE heals. Druids and priests both have a decent AE heal, but for chain heal to be effective, you need to target it, since it heals the first target more than the successive targets and it doesn't hit all group members.

With priests or druids, you can simply choose to have one party member as the static AE heal target - which means another decision you don't have to think about.

The thing about group synergy is that unless you're raiding, you don't need any synergies. It's nice with tremor and heroism and haste/flametongue/WoA etc etc, but it's not needed. You can faceroll-farm heroics with the current emblem gear with any tank / healer / 3 x dps (since you way way outgear the content), so the synergy is only needed for the first runs until you gear up and even then it's not required, it just makes things a bit easier.

On the other had, a group that plays well in terms of mechanics and require less micromanagement is more enjoyable to play (IMO), since it less you focus more on the encounter and less on pressing the right buttons.

I've done paladin, priest and 3 x rogues and had aboslutely zero problems except for a few annoying encounters with AE mechanics (and boy was I glad I had a priest at that time) - like that heroic-only boss in nexus who does an insanely annoying combo of AE fear and whirlwind that will one-shot blue geared melees.