CNJ/WHM is the simplest to learn- raw power, no special mechanics or quirks. You can focus on healing or doing damage as you need to without the extra overhead that comes with playing SCH and AST.
1. Mind, comes naturally on all the shared caster/healer gear and of course healer-specific gear. It affects the potency of your heals and your DPS spells, so get as much of it as you can. Healers care about having good weapons too- try not to slack off on upgrading now and again just because you're not a damage-oriented role.
2. Do: keep people alive, help out with damage if no one's at risk of dying if you toss a few DPS spells, mind your aggro (heals generate a lot of it!) Don't: over-heal to stave off boredom, cast HoTs (Regen, Aspected Benefic) before or during pulls- wait for the tank to stop and tag everything before you start healing in earnest
3. Number one, keep people alive. Do whatever it takes to save people despite their best efforts to kill themselves. Number two, help out with damage if you're sure you can do so without people dying. You'll get a better feel for when you can DPS safely as you play more. Take it easy at the start and get more comfortable with it as you go along. Number three, some fights, people will expect you to handle mechanics so DPS can keep hitting the boss, like the second boss of Stone Vigil. Learn what they are and if you aren't sure, don't be afraid to ask. Most people would rather take the time to explain rather than risk wiping and having to start all over again. Number four, tanks usually pull big. If your gear isn't up to snuff for that say something at the start to prevent tears and salt from wiping.
If you're ever feeling overwhelmed doing mechanics, trying to save people, and trying to throw out some damage, just focus on keeping people up. If that means letting someone sit at half health or less for a while then so be it. You're there to keep people alive, not full HP all the time.