Convert Existing Site to CMS

I have an existing custom website that I want to convert to a CMS site such as Wordpress or Joomla. The existing site is built using multiple layered templates built in Dreamweaver CS5 and I would like to have a similar structure on the new CMS site, either Wordpress or Joomla. The existing templates includes a main template, approximately 4 category templates, and about 1-3 subcategory templates under each category template. Any of the parent templates affect the child templates. There are php includes built into each template that pull in html, css, or javascript to control navigation, layout, etc and which affect all template dependent webpages. As in the existing site, the new site needs to have certain areas reserved within the category templates to easily post a message or other content to all of the dependent pages of the template. The only part of the subcategory templates that are editable are meta tags, content, and specially reserved areas for javascript specific to the page. One particular category has subcategories that have the editable content section displayed as tabs to help organize the information and reduce scrolling. I'd like to keep this tab feature, but I'm open to other options. Since pages under subcategories can share certain repeatable content in thee tabs, this repeatable content needs to have a dedicated place to be edited (currently done by using php include files). The CMS needs to utilize similar template functionality and structure as the current site so that updating content is easily done at any template level and at the individual page level. The new site needs to have similar navigation categories and it needs to work seamlessly and be responsive both in mobile and desktop. The existing site uses a MySQL database to pull in events and dates into the content areas. I want to keep the same functionality on the new site so we would reuse this same code as appropriate. I prefer to work with a single independent contractor rather than an employee of a larger group. Please let me know which arrangement you work under. Thank you for your interest.