I'm going to give you my general view of WotLK up to now (before Ulduar patch) as a healing paladin (I didn't play anything else seriously in raid until now).
This is more an indication of the order in which you should try things. I'm considering you are not in a big guild already farming content, and you just got to 80 and your guild is thinking of starting raids (yes you're late but there is nothing bad with being slow, that does not mean you can not be a good and smart player).
* = dumb, can be done in blue and is the ideal start to gear you up
** = require a bit of stuff or quality play
*** = require raid coordination and awareness
Archavon normal/heroic *
Sartharion normal/heroic * (** with one drake up, *** with more)
Malygos normal/heroic ** to *** (this is probably the toughest fight of LK, but for Sartha 2/3 drakes up)
Anub'Rekhan normal/heroic *
Grand Widow Faerlina normal/heroic *
Maexxna normal/heroic *
Instructor Razuvious normal * heroic **
Gothik the Harvester normal * heroic **
The Four Horsemen normal * heroic **
Noth the Plaguebringer normal/heroic *
Heigan the Unclean normal/heroic * (yes you need to learn the dance :p)
Loatheb normal/heroic * (if your healers are smart)
Patchwerk normal * heroic **
Grobbulus normal ** heroic *
Gluth normal/heroic *** (you need 1 or 2 people to kite these adds)
Thaddius normal/heroic *** (dumb raider = wipe)
Sapphiron normal/heroic *
Kel'Thuzad normal/heroic ** (who's going to die in these huge red beams anyway ?)
From a healer, especially paladin, point of view, some fights can be extremely frustrating. Paladins are very bad at healing while moving, and some fights really require that (Malygos Vortex anyone ?).
I would advise running most of the 10 men content with 2 healers (3 if you're learning but they will get borred), and the 25 men with 4-6 depending on your gear (don't go over 6 or they will fall asleep).
A few fights are a little challenging on the healing side more than on other aspects.
Loatheb : requires some precast/smartness, you'll need to use these shields more than any other fight
Saphiron : blizzard is bad for a paladin, know when to endure to get your heal out
Kel'thuzad : 4s to heal in a Frost Blast, if your raid is bad at interupting KT casts, you'll need to have awake healers
4 Horsemen (heroic, normal is a sad joke compared) : the "back tanks" are going to endure a ton of damage, not hard but surprising at first
Malygos : Vortex is a sad mechanic that renders a paladin nearly completely useless, be warned that most raids on 10 men will not use a paladin healer in this fight, just because of this stupid phases
And a last word to end ... learn to love your Beacon !
Have fun, earn cool achievements, that's the best to do while waiting for Ulduar.