Whatever you have, one of your rings is going to get replaced by your Violet Signet as soon as you hit Honored with the Violet Eye (which doesn't take long), or quite possibly even at Friendly, depending. But you'll have to wear something before then; here are some good options. Don't worry too much about getting two of these – one of these and a decent quest reward or whatever else you've happened to pick up will do fine until you get your Violet Signet.
Ring enchants are enchanter-only, so you probably already know what to use if you have the option, but it's Healing. Not too expensive.
- Primal Mooncloth Belt
- Seriously, I still haven't convinced you to go PMC tailoring? Fine, Black Belt of Knowledge (tailoring, 6 Bolts of Imbued Netherweave, 14 Primal mana, 1 Primal Nether) is pretty good, even though it has no +healing - the mp5 and spirit make up for it.
- Cord of Reconstruction (Kael'thas, Magister's Terrace) is also not bad.
This is one slot where the Hallowed is actually a little deficient, due to spending so much of its budget on int and mp5.
Silver/Golden Spellthread, made by Aldor tailors. Use the Silver on Haramad's, Golden on anything better.
There are a few options here that are quite close in terms of quality.
There aren't any amazing boot enchants for priests; Boar's Speed is generally recommended for the stamina and helping you get out of AoEs or whatever. I wouldn't bother with this on anything pre-raid.
Typically, a one-handed weapon plus an off-hand tends to be better for a priest than a two-handed weapon. There are some decent staves out there, notable the Serpentcrest Life-Staff, but any of these 1h weapons paired with any of these off-hands easily do better.
- One-handed weapons:
All caster weapon enchants can be put on either one- or two-handed weapons; there are no off-hand enchants. Major Healing is probably the best, and I'd say worth putting on any of the above weapons.
- If you're an alchemist, congratulations: you now have access to the best healing trinket in the game (thanks, Matthew G): Reedeemer's Alchemist Stone. A mere 6 Primal Life and 2 Nether Vortices, on top of your Alchemist's Stone, will get you a trinket you will not take off until Wrath (or until you respec Shadow). Like the Blue Dragon below, this one is great because it's passive; you can't forget to activate it. And getting a little extra out of those mana pots is nothing to sneeze at.
- If you happen to be a jewelcrafter, Figurine - Seaspray Albatross is awesome. But you probably know that already.
Darkmoon Card: Blue Dragon. Probably the second-best investment I ever made as a healing priest (the first being getting tailoring to 375 and making my PMC set). This is obtained by turning a full Beasts Deck (Ace through Eight) in to the Darkmoon Faire. It can be hard to find the Ace of Beasts these days, since it drops only from the Beast in UBRS, and that's not a terribly popular instance right now. But keep checking the AH and the trade channel, or con your guildies into three-manning the place with you if you can. The other cards should not be very hard to grab off the AH.
Once you do get the trinket, you will notice that it procs on anything. Making bolts of cloth, spending talent points, buffing, and so on. It's really a great trinket, all the more so because it's fairly passive - you don't have to remember to activate it on purpose. You wouldn't think something from pre-BC would be so competitive, but this thing is fantastic.
- Essence of the Martyr (41 BoJ)
- Bangle of Endless Blessings (Warp Splinter, Botanica). One of the few things left on my shopping list for 5-mans, this thing is another hard-to-replace-before-25-mans item. Many priests hate Botanica simply because they ran it so much to get this to drop. It is, however, a great instance for fast badges, and the Bangle drops on normal or heroic.
- Lower City Prayerbook (Lower City revered). For such an easily obtainable trinket, this thing is quite nice. Remember to use it whenever it's up and you're about to cast; a one-minute cooldown goes fast. Like most trinkets, it doesn't trigger the global cooldown, so you can slam your trinket button and immediately start casting. It's also possible to macro the trinket with a healing spell so it gets used automatically whenever it's ready; see this Wowhead comment thread for details.
The first rule of gems is: ignore the socket bonus. 95% of the time, matching gem colors, unless you were going to do it anyway, is not worth getting the +2 int or whatever. There aren't really any great gems to match yellow sockets; the best ones are probably the "luminous" series.
The best priest gems, by a considerable margin, are the "purified" series:
These are purple gems, so they match both red and blue sockets. I'd say go ahead and toss these in all your slots unless the set bonus makes it worth going to yellow gems.
As for what quality to buy, that's between you and your bank, but obviously don't put green-quality gems in gear that will last you a while - the difference may seem small, but that extra 2 healing and 1 spirit per gem really adds up. Purified Shadow Pearls are relatively cheap as blue-quality gems go. Most JCs will be willing to do the recipe for a small tip; it's taught by the gem trainer, so every JC should have it.
And there you have it! If you're wearing all or mostly items from the above list, you should be ready to make your way through the halls of Karazhan and have a blast. Your stats should probably be something like +1400 healing, 400 spirit, fully buffed.
I'd like to leave you with a couple of great resources to which I am deeply indebted for the information on which this post is largely based:
Check those out when you have some time for indispensable information.