Firstly get to grips with disc play that is so much more important than gear. How much you use pw:s and how well you manage your mana will determine what content you can heal.
The second biggest problem I see is people not utilizing the other tools they have; PoM is an excellent spell and very efficient, Penance is more efficient then flash heal. In with this there's also the fact that alot of priests do not try to increase their use of Hymn of hope and Shadow fiend, you may find saving one and using the other allows you to have a safety net but most priests will use both at the same time(as it gives more regen!) the trick here is fight lengths getting 2 shadow fiends is much better than one but this is hard to accomplish however just using these spells makes mana life so much easier.
In the beginning you will find mana being somewhat tight and without access to trinkets from Ulduar you will probably need int gems in your gear and the insightful meta gem. The int trinket from ToC 5 heroic is a nice starting trinket.
Disc has no real requirements for stats as haste cap is easy enough to get in 213 level gear. Haste is not a priority for disc.
In terms of when you are ready for ICC? generally that will be when you are in mostly 245 gear especially if you aren't in a guild but if you prove yourself a good healer to people you may have a lower requirement. In mostly 232 gear you could manage, then the question falls to the person taking you.