Wordpress is a fully capable blog, but we're trying to brand the way it looks, implement some discovery widgets that lead back to our actual site, and also add some features.
Basically, we want to be able to edit the HTML and potentially more, but Wordpress.com doesn't let you do this.
Wordpress.com is a hosted implementation of Wordpress, which is available at wordpress.org. It sounds like you should research the available blog platforms out there. You can google search "top blog platforms 2014" or something similar to get an idea of what's possible.
The upside of Wordpress is that there are thousands of themes and plugins that come close to what you want. The downside of Wordpress (especially on this website) is that many developers and designers are tired of it. The code is bloated but will probably be your best bet to use because of the large community surrounding it. You can edit anything in the self-installed version, but you can also break it which is why wordpress.com doesn't let you edit the HTML.
Do a google search of "Best _____ Premium Wordpress theme" or "best ____ wordpress plugin" with whatever your ideas are and see what comes up.
I have a wordpress blog for my startup. If you download the wordpress source code from wordpress.org and install it on your server (say on Amazon EC2) then you absolutely can customize the HTML, look/feel, etc and add widgets / features.
You will probably need to involve a wordpress theme developer to help you edit the HTML and get it the way you want it.
I'm not using Wordpress myself because I use my own blog/news script, but I customized Wordpress for some clients and the theme and plugin API lets you completely change the way a Wordpress blog looks. Wordpress has a couple of downsides but lack of customizability isn't one of them.
Basically, we want to be able to edit the HTML and potentially more, but Wordpress.com doesn't let you do this.