I want to start playing wow again. I want to be a healer. What is a good class for healing. Not pvp, instances, and raids. I am not biased horde vs alliance.

One thing also. What is a good class AND race. I need the race also!
I wasn't too clear. I meant I am not doing pvp.

priest hands down

For alliance = Shaman any race because they have earth shield and they can put it on tank so if someone is also getting killed they can heal the dps without having to worry about tank, now if multiple people are dieing they also have chain heal and much more types of heals,
Druid isn't recommended for level 85 but before that they do amazing heals and have so many instant healing spells you just have to be aware of how to use them.

For Horde= Blood Elves start out with lots and lots of intellect but they mostly only effect priests and paladins make sure both are holy and advantages are high crit heals and multi heals so ull never ever have to worry about dead tanks or dps

You might want to try Priest for healing. They have the most versatility because you can heal as Disc or Holy. You can also level as Shadow and still be an effective healer, while pretty much using the same gear.

For Alliance, you should probably choose Human for Diplomacy and The Human Spirit. Diplomacy will increase your Reputation gains which will allow you to get Epics you get from Exalted a lot quicker. The Human Spirit increases your Spirit, which is the most important stat for Priests.

For Horde, Troll is probably best because of Berserking. Berserking makes you cast faster, so if your party is in a tight spot, you can cast Berserking and spam Prayer of Healing. The only problem with this is that you have to remember to use this ability. If you feel like you're going to forget then you're better off sticking with Human.

Troll- priest or druid
Human- priest or druid
But I'd prefer Blood Elf Priest because they start with the highest intelligence

Blood Elf Paladin.