I ran a Balance Druid and 4 shaman (2 dual spec resto when required) to 68 or so. Then I shelved the druid and picked up my pally tank. Shaman are an easy combo as they can all drop AOE heal totems, for healing I had one resto focus my tank type toon and run a cast sequence of using a chain heal every third spell.

You do want at a minimum a heal toon (shaman, paladin, priest, druid) and a tank toon (warrior, pally, druid) to be able to do random dungeons for gear and XPs by self queuing. Fewer classes limit you on what gear drops but are also easier to syncronize than different classes.