@hytare and @yolo
You can have a brand page without a personal profile, although FB doesn’t publicize that fact. One of my clients has it, so I know it exists (and it works fine, too).
For a company, I suggest creating a dedicated email address just for Facebook, such as firstname.lastname@example.org, and a dedicated password (that you’ll make nice and secure and change often).
If you trust your Facebook account admins, you can give them access to the email address and password. If you don’t trust them, just make them a page admin and keep the login info to yourself. Page admins can do most things on your brand page without having to log in directly to the account.
The only thing I’ve had trouble doing as a page admin (without direct access) is monitoring the full statistics of a Facebook ad campaign.
Once you’ve created your account (try not to think of it as a personal profile), don’t put anything in the personal profile part of your account; just go ahead and create your Facebook brand/fan page. Use your brand page only and ignore the personal profile.