Help migrating website from one VPS to another

Our site is currently hosted on a VPS that we want to migrate away from. It's a live wordpress website, has SSL, uses CloudFlare and I have full access to everything including the cPanel of the VPS and wordpress backend.

I'm looking to move the site to Amazon AWS Lightsail, unless I receive advice to the contrary. We have an active Amazon AWS account which I also have full access to and am comfortable using the AWS interface but am not a developer.

I would ideally like somebody to take me through the process of migrating the website step by step, setting up the VPS on Amazon with me, configuring everything etc. The reason for this is mainly because I have a .pem file to access the AWS and am hesitant to provide that to anybody else. If you could show me how to create a separate access for you so that you can only access the necessary VPS area then help me do that and i can give you access.

I'm very technical, but not a coder or developer. If it was just transferring the site from one web host to another, i could do that, but I've never managed a VPS before. It would be great if somebody was available over Skype to take me through each step and screen share as necessary.

Looking forward to hearing from you. If you quote, please detail whether you would help me do it, or if you would need access yourself. I'm looking to do this over the weekend, so let me know your availability please (I'm guessing if we're corresponding over Skype then it'll be a few conversations at various times, while files transfer and things setup etc).

Thanks.