If you don't have a lot of time, than I think rep grinds will help you a lot. For instance, Wildhammer has some nice 346 items on revered and a good 359 boots on exalted. You can quest your way up and than continue with dailies which take no more than 10 to 15 minutes a day.
There are more reps that are really easy to get to revered which will give you pretty good 346 items. Try to get them. Invest a bit of time each time you log in and you'll get there. After that, you can easily do heroics.
However, do notice that most heroics take more than 1 hour to complete. This can even range up to 2 or 3 hours if you have a large heroic and / or if your group wipes a lot. Especially when gear is not really great yet. Use CC a lot in there.
As soon as you have 346 pieces, do enchant them. For the 333, maybe get some "cheaper" enchants. Befriend with an enchanter and send him your boe greenies. That way you get free enchanting material without investing time.
Hope this helps.