I'm making this guide just from my own experience as what I think should be the fastest way to get yourself ready for Heroics / Raids in Cata. All of the things below are based on my own experience if you'd like me to add/remove/change something please leave a comment as I'm trying to make this for the general good First off you reached lvl 80 (grats!)
What should be in your best interrest now is making yourself a nice questing route to lvl through to 85, one which is also fastest to making you geared ready. leveling by quests may take a little bit longer than running FB's to get to 85 but if you did all that hard and lonely questing you will be in Heroics much faster than those who didnt.You might ask why nog running dungeons: Questing is a lot faster than running dungeons as the green quest rewards you get from Twilight Highlands are already better and higher in ilvl then the blue's from lvl 80-83,5 dungeons. In other expensions those ilvl werent that important as now, as soon as you hitted the lvl cap you were able to go anywhere (pre dungeon finder time). Below Are the links of all the quartermasters of the Cata factions:80-82
Mt. Hyal Questing gets you to revered
Vash Questing gets you to Honored82-84
Maelstrom Questing gets you to Honored
Uldum Questing gets you to Honored84-85
Twilight Highlands Questing gets you to HonoredThe item's that would be of most interest in the beginning are all those that are ilvl 333 or higher (Revered / Exalted) some of the Honored items can also be usefull to boost up that ilvl by replacing the crappy green one you couldnt get rid off.
Once you picked your Ideal item/quest route its time to put that into action, Off course it is also possible to do multiple routes at same e.g. both Hyal and Vash, Uldum and then Twilight instead or only Hyal, Uldum, Twilight.I'd strongly recommend for everyone to finish the Twilight Highlands questing area as some of the quests there already provide you with item rewards of ilvl 333.
Once you hit 85 it is time for you to check up on all your quatermasters and get yourself geared most of you also should have some justice points which got exchanged from the old Emblems of Wotlk. Go to your quatermasters gear first and then spend those Justice points you had saved up. Dont worry those JP will be refilled quickly and are not hard to get back.Some of your quatermasters may have items that are still good for you but not to your class e.g. hunters could benefit from those rogue leather items as well. I'd recommend you to buy those as well just for the sake of boosting you ilvl you can replace those once your in Heroic.
At this time you should be well on your way to an ilvl 329. You could do some lvl 85 dungeons or check the AH for a BOE that would fill your last slot of a lower item to replace. From now on you could also buy pvp gear for the slots that are missing as pvp gear has high ilvl value. When doing dungeons don't forget to buy and wear those tabards from the factions that you'd like to get rep from those epic's are ilvl 359 which is higher then gear from Heroics, you use those epics to get ready for raiding ! As a tank or healer i'd recommend you to get some dps gear as well, as in the beginning your first Heroics will be most likely as DPS anyway to be able to learn the fights, and go. As Heroics are harder now than beforelast night (26-7-11) We had 3 guild groups mixed with pug (4-4-2 guildmembers) Doing Heroics, these numbers will hopefully only increase. As these groups all have experienced players from guild now it doesn't matter if you tricked yourself into an ilvl 329 by using non your class items you can always do Heroics with us as were happy to help you into a Tanking/DPSing/Healing machine!
Thats it for now... Hoping this information was usefull to you and to be able to raid with you soon !