Your Priest begins her career in leather gear and wielding a mace. Eventually, you'll be working your way up to chain armor and gain the ability to sport a shield, as well. For now, just about any manastone or stat, with the exception of shield defense, will help supplement your leveling. Evasion and physical crit help when you're meleeing, HP and MP keep you off your butt and limit your downtime, while magic boost augments your offensive spells. It should be noted that as of version 1.5.8, spells cannot crit and magic boost does not effect healing spells.
If your goal is to be a party healer, you may want to hoard any cloth gear you happen across, as it will typically provide much more MP and concentration than leather or even chain. Of course, this shouldn't be much of an issue until much later in the levels.
If you've already tried one of the other classes, you may find the leveling process of a Priest a slow and tedious affair. You are pretty difficult to kill, but the trade off to such sturdiness is that you may find yourself boring mobs to death. Fear not: the action will ramp up and following Ascension, leveling for both the Cleric and Chanter classes gets much more interesting.