I can't speak to all heroics, but my belief is that they are ALL about refining technique.

So, I'd recommend Gundrak as the one to focus on initially. Once I perfected my technique, I could farm five badges in under 2 hours. (Probably faster, but I'm being a big cautious.) There are a ton of upgrades in Gundrak for my mixed team. I then went on to UK and find that a pretty easy dungeon now too. However, there's a ton more trash to clear in UK than Gundrak.

I need to expand to VH and CoS. My few tries at CoS I was able to get the first two bosses easily. However, getting past the dragonkin in the first building was killing me. Need to try it again as I've gotten some gear upgrades.

So, farm Gundrak for five badges per day, upgrade gear, and expand to other Heroics. My two coppers.