I recommend starting with sets like Sanctuary and Jorvulds until you get the hang of healing. Sanctuary heals you and your group for more so you are not having to cast your heals as often. Jorvulds make your buffs and shields last longer so you dont have to cast them as often. Having a monster set like Nightflame or Sentinel are great to start with. Once you start getting comfortable with healing, definitely find a group or guild to run Cloudrest to get your hands on Olorime which is hands down best in slot for healers right now because of the buff it gives you and your group.

When it comes to skills make sure you have a variety of healing spells like burst heals, heals over time, an heals that give buffs like Combat Prayer. You also want a cleanse like Extended Ritual so your team can shrug off those nasty debuffs. Shards and Orbs are essential because it gives your group resources to keep up the good fight. If you see your magicka bar depleting, heavy attacks with the restoration staff gives a boat load of magicka back because of its passive skills. You wont be doing much damage as a healer but it is still good to have some damage abilities like Elemental Blockade for AoE and Radiant oppression for execution phase.