See if you can maybe find a studio that has one or two classes a week that are donation-based. It's not uncommon. I would recommend either Anusara or Iyengar because of their focus on alignment. Any practice that overlooks the foundation is inviting injury, and I include everything in that, not just yoga - ordinary American-style strength training, CrossFit, Pilates, etc. Anusara might serve your particular needs best because of their emphasis on opening the heart.

As far as the energetic aspects, I'm a big believer (and have tons of experience) in collective energy, so from that point of view I prefer a class. But if you get a really good teacher to show you the basics four or five times so you really have a sense of what to do, then there's nothing wrong with practicing at home, since you can keep your teacher's alignment cues in your head regardless of what the DVD is telling you to do - and then it's whatever works best for you on an emotional and energetic level. For some people it's easier to tune out distractions when they're alone.