This is the setup I use for my Khajiit healer, Clan Mother Kitta-Ko.

Before a fight, I typically spam some Rapid Regen to get the group ready, then use Combat Prayer once we've started, then a Ritual for some extra HoTs and DPS. I then typically swap to to DW and use Shards for a bit of AoE and to help any stam users in the group, followed by Puncturing Sweeps. I swap between these two bars, throwing out Combat Prayers, BoLs, and Rapid Regens as needed, and using Repentance as enemies drop. I also tend to use my comet on particularly big pulls for extra DPS and DoT. If there are no adds for a fight, I switch out my Repentance for Healing Springs.

During boss fights, I make sure to keep Purifying Light up, not only for the DPS, but for the little extra healing it gives as well.

As for ults, I usually rotate between Solar Prison, Ice Comet, and Practiced Incantation depending on the dungeon and/or boss fight.

ARMOR: 5pc SPC, 5pc Healer's Habit
WEAPONS: DW Swords Magnus' Gift, Master's Restoration Staff
FOOD: Witchmother's Potent Brew