Heroic 5 mans should only require like ilevel 430 or something to get in to, you should be able to get that just from quest gear you got while leveling.
In order to get LFR you need ilevel 460 to start, which you can technically get by just doing Heroic 5 mans.
Doing Sha of Anger is also something you can do, try to find a group, the first time you get kill him you get a quest item for 476 boots and he has a chance to drop 496 tier gloves or legs.
Reps: The most important is Golden Lotus. I would recommend the wowhead gear guild found here for a list of gear to look for so you know what reps you need to grind, you probably don't have to do all of them, I know I haven't.