My suggestion for integrating with websites is pretty simple. We suggest keeping Blesta separate, and simply updating the templates to match your website. They will be independent, but look seamless.
~/app/views/client/bootstrap/structure.pdt contains the header and footer of the client area and front facing pages. Usually all you have to do is modify this file, and sometimes add a new overrides.css file with your CSS changes to overwrite any styles you need to.
We recommend running Blesta on a server by itself if possible, at a subdomain like my.domain.com, or account.domain.com, billing.domain.com, etc. This way, if there is a vulnerability in your website, it won't affect your customer data.