Hi, I'm Sernon from EA.
This is the single best resource I've ever seen for gearing up through Kara.
The most important thing you'll need to work on is getting your defense up to 485 (uncrittable in heroic). You can ignore strength and spell damage for now (spell damage is nice, but only if you have the survivability to wear it).
The questline to be keyed for Arcatraz has a very nice belt reward,
here. Keepers of Time rep gives a very nice leg piece, as well as a vital glyph, the glyph of the defender. On top of that, they have the continuum blade... all this comes at revered, which is only about 5 runs, thanks to very generous rep from the questline in there. Not only that, but that questline gets you a decent starter tanking ring....
So, in short: Do the Keepers of Time questline. Then get your arc key. These are also 2/4 of the instances you need for your kara key, which will help your rep with them, and get you another nice tanking ring.
After that, feel free to send a tell to me or Suzumiya (my pally) with more questions.