Well, I don’t have any personal experience as a customer with NetworkSolutions, but looking over their package deals, you may be able to get more bang for your buck if you shop around a little bit.
Losing everything can be tragic if it happens. As far as email functionality, almost all servers provide MX records for your domain so that any mail addressed to @yourdoman.url gets delivered to that mailbox (if it is set up) or forwarded to a specified email address. You can configure these in cPanel (or whatever hosting app your service provider uses). There may be a time frame of interrupted service where email sent to you during that period would be orphaned, but as long as you back up your email before you move, you shouldn’t lose a thing.
Before you pull that trigger, you may want to install XAMPP on your local machine, get MODx up and running, then as you have time, translate your site into MODx-ianeeze.

Then, when you have your site fully converted and working on your local XAMPP server, find a host with Linux, Apache, MySQL and PHP, export your local site’s Database, upload your modx installation’s folders to your new web root via FTP (you would need to upload the index.php, /assets/, /manager/, etc... that stuff), import the database into your new host (probably using phpMyAdmin or the like) and your good to go!
No rush to quickly get the MODx site up, plus it gives you some time to shop around for a hosting package you like while you are creating your site locally.
There are some other intricacies involved in switching from local server to remotely hosted server, but when you get to that point, I would be more than happy to help.
-sD-
Dr. Scotty Delicious, Scientist.