Best way to transition from HTML site to new WordPress version

Many of the projects I will be working on in WordPress involve taking an existing site and using the content to develop a new WordPress version. For example, a current client has a site on GoDaddy and we need to create a new WordPress site on HostGator using the URL of the old site. It seems like it would be best to move the existing site and URL to HostGator first and then develop a WordPress site for that URL. I am not sure how to then make the WordPress version of the site be the official site for that URL, rather than just a blog associated with the old site. I also want to make sure I do this in a way that won’t terribly compromise the SEO ranking the old site has established. I understand that SEO will be affected but I want to minimize this as much as possible.

I apologize if these are basic questions but I wasn’t able to find information in the FAQs about the best way to handle site transitions to WordPress.