Hello, I read your requirements and I feel I am the one to do this job, you could do a test site to go gradually covering each of their needs until the final product is finished.
I am programmer with skills in html5, javascript, jquery ... in the area of CMS, I have skills in wordpress, Joomla, Drupal and Magento.
If you do not agree with what I ask as a reward, could discuss a better price that fits your budget.