I want to start building relationships with influencers/bloggers in my industry; when I interact by commenting on their blog site, on twitter, facebook, etc. should I be using my personal account or should I be using my website brand account?
Without question, you need to brand and market both. It's an ongoing effort that will require effort, patience, and time.
I launched our firm in 2009 and at that time no one in the WordPress community new me or my agency. I started marketing the company first, but realized it was much easier to market myself as the face of the company.
Overtime I realized people respected the company and our work, but they related to me the person. The more I infused myself in our marketing efforts, the faster the company branding grew.
Bloggers and social media users in general will support and become brand ambassadors for the company, but they do so because they like the people behind it.