It's not necessary to grind any reps. It's one pathway.
I've levelled 2 to 90. First one needed 1 piece of gear to queue for heroics. I was surprised that the second didn't need any and could queue immediately.
All classes can get ilvl 476 chest and hands crafted. You get ilvl 476 boots off of Sha. 470 trinket off Direbrew. Those along with some heroic drops will easily meet the LFR bar.
If you do choose to get valor gear, then don't overload yourself in the process. Choose 1 faction and work on them. If you are ploughing all them at once not only are you over-capping valor but you are going to reach the rep requirement before you actually have the valor to spend. Look at your loot tables, decide the valor pieces you want, and make a plan.
It's easy to get overloaded. Don't do everything at once.