For a starter healer, the best set by far is Seducer. Just put 5 pieces (without Head and Shoulders) and update as you get the mats and better sets later. It takes just 3 traits to craft and it is on your capital zone so you can get it very early. I began crafting it as soon as I had the traits and never looked back.

I also complement with Torug's Pact Resto e Dual Wield. Those sets a good craftable sets with fewer traits required. Leave head and shoulders for monster sets or dropped sets, specially since there are excellent ones coming on One Tamriel update.

If you have more traits, Julianos and Kagrenec's Hope are the way to go for crafted sets for now.

The end goal should be the Spell Power Cure set, but from my own experience, it is VERY hard to farm since it only drops in White Gold Tower (WGT) and you need a good group that knows all the mechanics to get good runs there.

You can start at normal since sometimes it drops level 150 purple SPC, but the aim should be to get the 160 stuff in vet (well, at least until the One Tamriel update - it seems that after that normal WGT will drop blue 160 SPC that you can upgrade).

I like Willpower Arcane jewlery. It is expensive, but you can buy them at various Guild Traders in Craglorn and your alliance capital. Later on it will drop all the time, but not always with the right trait. I found that reduce Spell Cost is better than Magicka Recovery for jewlery, but it is just my feeling. Don't know if the math supports this. After you have a more endgame build, switch to Spell Power.

In the beggining, you can try both Magicka and Health enchantments on armor to see which suits you better. I find that my magicka never runs out with all magicka so sometimes I put a couple of Health enchantments to get more survavability in dungeons. For trials, enchant everything with Magicka.

As for the skills, focus on buffing, support and healing with some DPS / Execute if you have a good group that gives you time to do a little DPS.

As an example, my current rotation goes something like this:

From Resto bar:

1. Rapid Reneragion (RR) 2x (Resto skill line - it takes 2 casts for dungeons and 6 for trials since each cast gets 2 allies) - Increases allies health regeneration
2. Follow the tank and cast Extended Ritual / Ritual of Retribution in the middle of the fight - Heals allies inside the area AND does a little damage
3. Get to a good spot on the fight and cast Restoring Focus rune - restores magicka and increases your resistance
4. Remembrance (Ultimate) when things get ugly or your are low on magicka

Change to Dual Wield (2 swords) bar:

1. Throw Luminous Shards / Blazing Spear near the tank or at trash mobs to help clear them, if there is time - the tank can activate the synergy to recover Stamina, just keep them coming at him
2. Puncture Sweep your target until about 30% health if you have time and group's healt is good
3. Cast Radiant Oppression (aka Jesus' Beam) on targets or bosses if their health is very low (< 30%) - be aware to block and break the animation to cast Breath of Life if someone's health drops too low
4. Solar Prision / Meteor (Ultimate) if things are under control to help the DPSs

All the time:

1. Breath of Life if someone's health drops to 50-60% - RR and the Ritual SHOULD bring back everyone's healt to full from 70% if they don't stand in red AoE and you keep the buffs up
2. Every few seconds into the fight, cast Repentence after some enemies die to restore Health and Stamina for allies
3. Keep throwing Spears at the tank every few seconds and Repetence
4. Always move your eyes between the group healt bars, the AoEs and your magicka... It is crazy, but you get used to it.

This seems like a lot, but once you get the hang of it it is just a matter of paying attention on when to break the sequence when someone's health drops too low and then restart the cycle.

The ideal thing should be to have the Resto bar with your healing skills and the Dual Wield if some support and DPS. In practice, I find that I have to dual slot Breath of Life for most PUGs. With experienced players, you have time to switch bars and heal, so you can put some other DPS like Purifying Light / Power of the Light.

A few tips:

1. Keep an eye on the AoEs. If you see someone is not going to escape the AoE and you have magicka, cast BoL BEFORE to get them to full health. Sometimes this saves one-shot kills.
2. If your magicka gets too low, change to Resto bar and heavy attack any enemy to recover fast
3. Keep the buffs up! The Ritual is easy to see since it lights up the floor. RR makes your allies have a little golden glow, like little sparks coming out of their chest. Rune makes you all golden. Learn to notice this visual cues. Or just rebuff everything after the Ritual fades until you get more used with the times.
4. Pay attention to the tank! You need to keep him alive and supplied with Shards.
5. If things are under control, you can revive allies. If not, ask another one to do this while you heal.