Managing Director/Principal of Monkey Hill, LLC, an information security consultancy specialising in technical assurance and the architecture of information systems and security controls with the ability to communicate with a broad audience from management to junior staff, both the technically aware and the technology-averse alike. Thirty years of IT experience with 17 years of cybersecurity domain experience.
Moving the entire site (domain, site structure, etc.) intact to another hosting service will have not affect on your Google search rankings.
You need a SSL certificate. You can purchase these from many place or from your hosting service.
You need to install and configure the certificate on your web server.
I don't know what technical challenge you will face. I don't know your level of technical proficiency.
I have used CloudFlare for the last year to protect my web site from attacks.
CloudFlare’s technology automatically detects new attacks that arise against any website on its network.
Read more about CloudFlare's security features here: https://www.cloudflare.com/features-security