These next few items will last you a loooong way, so try and get your hands on them as soon as you can:

Energy earrings
Zealot mitts
Silk Mist Cape
Blood Stone
Justice Badge

Those basic items got lasted me ages from pre-dunes all the way to the Jungles.

As for other equipment, just try and get as much MP and MND as possible. I do put priority on MP over MND, but both are important to a WHM.

In party situations, you have 3 things to consider.

1) Healing (of course)
2) Buffing
3) Enfeebling

If there is no Red Mage in the party, always always always start off the battle with Dia/Slow/paralyze. This will make the battle go much much better. Also be sure to to throw out appropriate Bar-spells because these will save you from having to cure as much. So be sure to know which bar spell will benefit your party against a given monster. And make sure to always have protect/shell up.

As for healing, in the beginning it'll mostly just be throwing out Cure I after Cure I. But as you get higher up, you're gonna have to start deciding which cure will best conserve your MP while still keeping everyone healthy.

Once you get regen, you should cast it on the primary tank on every battle and if you can, on secondary tanks and other melees as well.

As for healing, I like healing with the < stpc > macro so that I can shuffle through my party and select who needs curing rather quickly. Be sure to have {Gather Together} in your Protectra/Shellra macro. I always think it's bad manners for a white mage to not have that in their macro and they just go shooting off buffs when the whole party isn't even gathered together.

I would post my macros for you but it's late and I'm tired.

When you get Haste, be sure to cast THAT on the tank/melees as well. Figuring out Haste cycles can be a bit tricky since the timer on it is a bit longer than other spells and conserving MP should still be kept in mind.