Hello...:-) I have checked out the 2 site samples and much to my surprise the [login to view URL] is built using the YooTheme Warp 6 framework with the Nano2 template. I use this all the time and customize...:-) I have been working with the YooTheme / Joomla software and extensions for 10 years (since Joomla 1.0).
I would definitely start with Joomla's (CMS) latest version. I would also start building on my server. I have a re-seller acoount through Hostgator and host approximately 80-100 sites on my server. You can view some of my sites from my online portfolio ( [login to view URL] ). I am currently doing updates to the site, so if there are any questions you can not find an answer to , let me know.
As for your site, if you can give me more details of the site, and what you are after, I would be happy to do a front page mock up for you before chosen...:-) Just supply me with enough details to get it started (logo, images, type of site, colors, etc.)
Thanks! I look forward to hearing back from you.
Sincerely,
karen