Boomkin is the only one i can think of. Even if you go another spec, with the talent row that gives you healing abilities, you can do both, plus have utility with the Azerite traits.
Do you want to be one of the more powerful classes and put up great numbers? If so then you want to be a Warlock as they will always have one of their specs in the top 3 or so.
If you want right now then either Lock, Shadow Priest, Ele Shammy or Boomkin.
If you are talking pvp then I am not sure as I don’t really pvp. Boomkin (and I believe ele shammy) have self heals. I know leveling my Boomkin alt I have 2 forms to heal. One that is instant and another you cast on yourself or others. Druid also has all 4 specs (tank, healer, rdb, melee). Lock is pure dps.
Not sure what you mean by varied rotation/priority as I assume all classes have their own set rotations.
I haven’t leveled my Shadow priest since level 90 so not sure how the leveling goes for them.
There is actually a good amount of small nuance in boomkin, once you get the right azerite traits. You need to keep alternating your spell casts to proc streaking stars, as well as monitoring arcanic pulsar stacks and pooling resources for when you get your free incarnation. Going starlord with a cancelaura macro adds even more to the spec.
Easy class to learn, but there are definitely things you can do to separate yourself from the mean.
Yea I suppose so, although it isn’t something I really think about too often. Starsurge hits like a truck, but outside of that the rest of the kit is there to build up for starsurges.