We have gone through your requirements. Is it a simple html website or a CMS? Also can you please specify the approx number of pages that need to be transferred to the new site. Sharing the url of the website will answer all our questions.
Recently, we have done similar projects like this. Transferring of contents is not difficult for web developers like us. We also deal in content writing, so your concern for good English is also catered. Please check your inbox for more information about us.