This is not an easy question to answer. The best thing to do, I think, would be to install SilverStripe on a test site, and check it out. (If you have no testsiteavailable, check out the existing SilverStripe CMS demo here].)
Yours is not a very large site, so I guess you could just copy your websites content into the CMS page by page. As for the theme: your HTML setup is somewhat dated, so you'd do well with an existing SilverStripe theme, and just add your header image and change the colors a bit...
There are modules and themes available here: http://www.silverstripe.org/extending-silverstripe/ Look for the userforms module that will let you create a (contact)form.
Take a look at the tutorials and ther documentation here: http://doc.silverstripe.org/framework/en/
If you are more experienced, checkout https://github.com/silverstripe-labs/silverstripe-sitetreeimporter. There is a static importer here That I haven't tested.