You may have to que up some normal to get into the item level window for heroic ques. But if you hit a few of the blue items in zones leveling up or hit 5 mans hard on the 80-85 range you probably are close if not there. If a little short look on the AH, the blue 346 gear is usually dirt cheap these days.
Que normal heroics until 346, it wont take long bc the JP can get you 359 stuff and drops you pick up along that time. Also, you will be getting valor, so the road to 378s starts to open as well and can pick up some stuff along the way there too.
Que for ZGs as well. Its drops are better than 346, although the ques sometimes aren’t as great. They also are a HAIR harder, I could consider it mostly a change up, but it does give better valor points over time.
Once you are in that 346-350 range just start hitting the infernos in the que. Use those stones to get high end stuff from last tier. Sometimes you will run into jerks that kick you… it happens… but most people are so worried about gogogogogogo that checking people isn’t to high on the list.
Try to find a BH10 and 25 each week. Most people don’t check them to tightly bc the boss is an absolute joke. Odds are low on a hit, but with it being class/spec runs mostly a drop means a hit most the time. Also scoops you up some valor as your eyes start to get tired of the 5 mans.
BOEs are an option but if you are totally fresh gold might be tight, but just food for thought – the 359 stuff and 378 stuff available there.
Rep also has some gear, I probably would aim mostly at getting your head and shoulder enchants handled first even though they may or may not have items you are looking for as a priority. In the long run this will make you happier once you start to gear up a bit.
It really is SUPER simple to get up to 370+ item level these days. From there normal GDKPs become an option/normal guilds looking for players/normal pugs. You might find your way into some heroic level Firelands runs as well, but don’t be disappointed if that doesn’t happen. GDKP road is usually ideal because you start getting cash even if you aren’t getting items right away, but I know some people dislike them… so just go with how YOU feel on that. BUT, once you hit this point you are there, you are mostly caught up and rocking and rolling.