Isn't this about what spec is better to level as?
Answer = discipline
Disc is far less gear dependent while leveling and in dungeons you are far more mana efficient and need to drink less. It isn't really even a competition. In 5 mans (which are all you can do leveling really) discipline heals a group just as well as holy. Group/AoE heals are also not that useful in 5 mans as they usually just waste mana. Glyph Penance and either FH or PW:S depending on healing preference.
Holy just uses too much mana and is based of large number and AoE heals that end up wasting your mana.
Some specs
LEVEL 60
http://www.wowhead.com/?talent#bVcbuhhVRhsfckt:Ab
LEVEL 70
http://www.wowhead.com/?talent#bVcbuhhVRGsffRt0x:Ab
LEVEL 80
http://www.wowhead.com/?talent#bVcbuhhVRIsffRt0xtc:Abm
Toward level 80 some people put those points from Divine Fury into Healing Focus and/or Spell Warding, I'd leave them in Divine Fury while leveling/doing 5 mans because I like to smite/holy fire mobs when bored/farming waiting for instances. Basically those 14 points in holy are up to you, but definitely get Inspiration and Desperate Prayer (saves you life more than you care to know).
EDIT: For More Info
I play a priest with both Holy and Disc spec/gear in a 11/12 ICC guild and I've raided priest since Vanilla. Holy is great in raids with 25 people, but until you're in 232+ gear you find yourself OOM more than you care to know, especially since your just now starting to play a priest and will be in 5 mans for a while.
Some discipline how to:
Discipline is about mitigating incoming damage first and foremost. You will never see yourself at the top of a meter, but that's ok. Your spells:
Power Word: Shield... just do it. This should be on your tank 100%. This mitigates a large ammount of damage, puts weakened soul on the tank (increase your healing), and returns ~90% of the mana cost back to you when it is fully absorbed. If you know AoE damage is coming to your group then use a bubble on everyone (no CD) and if absorbed most of the mana will make it back to you. Don't just bubble spam the DPS members because you can as this will eat through your mana. Also adds Renewed Hope to your party/raid.
Penance: Your "Go-to" spell. A quick healing burst that will put 3/3 Grace on the tank quickly. Best to use PW:S on the tank before this because Penance is affected by Borrowed Time and doesn't eat the charge so you can take advantage of the haste buff for Pennance and your next Flash Heal.
Flash Heal: Your spell of choice when the others are on cooldown.
Prayer of Mending: Like holy, this is a great heal that you don't even need to control. As a rule of thumb, keep this on cooldown on your tank.
Prayer of Healing: Use sparingly and only with Borrowed Time. If you're in a 5 man and the whole group needs a heal, use this.
Binding Heal: when you get this, use it when you and a target need heals. More healing and mana/time efficient that 2xFH. **As a side note, this spell offers more throughput than Flash Heal, so if you need bigger heals on a target more quickly and don't need to worry about mana, use this instead (all situational)**
Renew: Debated, but don't waste a GCD on this. Basically the only thing I use it for is Life-tapping warlocks.
There's not really a "rotation" but PW:S, PoM, Penance, FH in that order are the basics.
I can link some holy specs if you want to try. But I recommend giving disc a go first.