Supravirtual (the company I am representing) can design your website using (mainly) Joomla! but also Wordpress (when necessary). We can extend Joomla! by developing custom extensions (components, modules and plugins) that will fit to your needs perfectly.
The design can be chosen from any current examples, can be delivered to us (as one of the requirements) or it can be designed on-site.
The designed websites are responsive and optimized for search engines (on-page SEO).