As a healer you don't have he hard stat requirements that tanks and dps do. Shojindo's post gives a very comprehensive guide, but because it is very generalized you might end up over-preparing in some areas.
Depending on who you play with you can get into T1 expert instances sooner or later in terms of gear progression. If you're running them with friends or guildies who are willing to work together and know their stuff, then you can hit up T1s a little sooner than if you're doing a full pug.
As a Cleric healer one consideration you will want to take into mind is having two specs for healing T1s. Certain builds work better than others on specific bosses, and certain group setups work better with different builds. For example I healed T1s and T2s primarily as a 51 warden, but as a 51 warden I didn't have an aoe cleanse which made specific boss fights harder so I had a backup healing spec that did have an aoe cleanse form sentinel to deal with those situations. Also, while I very much enjoyed healing as 51 warden with friends and guildies, it was bad in pug groups that had terrible hate management because.
As for spec recommendations I would recommend a 32 purifier/32 sentinel (with the remaining spent as need), a primary sentinel with 30ish points spent into warden, and a 51 warden.
-Purifier/sentinel hybrid is pretty much the easiest to play spec and the best with bad pugs. Your primary heal is a talented restorative flame, you can take care of like aoe healing via surging flames, and you have the strong emergency tools to deal with bad hate management.
-Sentinel/warden is for people who like the purifier/sentinel style of play, but need some better aoe healing tools and need some instant cast hots to help them in boss fights that have a lot of movement.
-51 Warden/15 sentinel is my personal favorite for 5 mans. It is one of the most challenging builds to play correctly, but also has a lot of potential and can allow you to take on some bosses earlier than you would be able to with other builds. It has the strongest single target throughput, far superior 5 man aoe healing, and high mana efficiency. For all this gain you trade nearly all of your emergency tools. It can be terrible in bad pugs because you need 4 stacks of soothing stream on the tank before a fight begins, which can peel a pull off of him if he is bad. It has very limited options to deal with people who pull hate off the tank when they shouldn't.