Moving my domain without losing all of my e mails.

At the present time my website is a disaster. I cannot fix it nor can I pay anyone to create a new one for me. I want to take the website down completely, but I want to keep my domain name because I hope to be able to pay someone to create a website for me in a year or two. I have not had a decent website in a few years and that is my fault, but at the moment I am too busy writing and publishing books to do anything about it. I am having to pick my battles.

So, I have created an account at Hover.com to park my domain until I can use it again. However, I do not want to lose my e mail address as it is my author e mail address and it is how I keep in touch with my readers. Apparently Hover has a way to do that, but I am not certain how to start.

What do I have to do to unlock and transfer my domain and how can I do it and not lose my entire box of e mails?

I hate to leave homestead, but right now I have to make hard choices about where I spend my money and how I can create and maintain my brand.

Any and all help is appreciated.