If you want a quick rundown of how to burn through the heroic gearing process, this is what I did.
Stack haste, buy vp bracers and boots with other characters, use your own vp to buy the wand since its only 750. Use a little gold and pick up tsunami and any of the 378 boe pieces because they aren't that expensive. Even 353 and 359s work fine. Basically anything to boost ilvl and int.
Make sure your addons are correct. Power auras for Pom and aa cooldowns; omni cc and gridsideicons for buff/debuff tracking.
If you get your ilvl up to 372 from boe gear, grab a couple friends and have them go with you through lfr and roll need on everything. Doesn't matter if you need it or not, you can trade people for other drops you don't win.
Then continue to hour of twilight heroics possibly with a friend or two at first. The questlines alone provide you with a few solid upgrades.
Oh, and always gear a shadow spec too. You want to be able to say that you can swing dps. This will get you into twice as many ds10s
Don't forget about dispel. You mentioned specifically how tough the first pull in HoO is. That big guy that stands in the back and casts, after he gets done channeling he puts a really mean buff up on himself that deals a LOT of AoE damage. Dispel it. It makes that pull a lot easier. Every time you come across that mob be ready to dispel. Ditto for the Throne of Tides gauntlets, and the swell cast by the big elementals there.
Don't forget to dispel/cure disease the players in your group. It's almost always more mana and time efficient than healing through whatever they have.**
**disclaimer: There are some rare situations where, when no one but the tank and that one dotted person are taking damage, casting a PoM and letting it bounce between the two is preferable.
I'm guessing your getting kicked due to gear. The same thing happened to my alt priest (and my main priest is 8/8 hc so I'm pretty sure I was "doing it rite").
If you've got a main/some gold/nice friends get a few BoE pieces and make sure to gem/enchant them. Tsunami is good and may be cheap depending on your servers economy. You could also try running with a few people you know maybe - real ID friends work too if you have friends on other servers. Helps a lot when your gear isn't that great if you have people in your group you know who won't rage if you need a mana break after a rough pull.
I'd suggest like other posters have speccing DPS if you can't get some BoE stuff. Your far less likely to get kicked as a dps with some dodgy enchants/"low" gear than a healer.
UI/Keybinding wise I'd just use whatever your most comfy with in 5mans. If you decide to start raiding on your priest it sounds like you've already got a great UI setup with rapture/PoM tracking and some mouseover macros (or clique if you swing that way) would let you do things a tiny bit faster than clicking.
Statwise haste/mastery/crit depend on personal preference and playstyle imo for disc. I like a mix between haste and mastery and have enough int to have a decent crit chance without forging for it. I spend a lot of my time tank healing in raids though
Gear wise a Tsunami is godly if you have the spare gold. The 2set tier from justice is really good as well. If your particuarly rich the crafted dragonsoul bracers are really really (really) good as well. Healing wise I find it much easier (no matter what toon) to heal the Hour of Twilight heroics. The only thing to watch is squishy tanks at the last boss in end time who think they can tank all 4 mobs with no interrupts or cooldowns :P
Once you get good enough gear you can pretty much just smite your way through heroics and occasionally throw a heal on a ranged whose over in china
Thanks, everyone for all the advice. My gear is still progressing, and like I said, I don't get to play much, but it's coming along. Done a few heroics, PuGs, even, and they've been successful. Did a few more Normals before jumping back into the heroic mess to get a couple more pieces of JP gear.
Also, at my current gear level, it seems easier for me to keep the tank and everyone else up with the SoS spec. My SP and Haste just isn't high enough yet to be able to do that much healing through Atonement. It will get there, I know, but SoS is working better for me at the moment. Anywho, thanks!!