Ubercart

I can't speak specifically of migrating E-Commerce to Ubercart, but with migration you have a four stage process really:

• Understanding your Data
• Getting your data into a common format
• Migrating/moving/transferring your data
• Testing/auditing the results

This tutorial is good for giving an overview of migration to drupal, but as you already have the data in a common format (your MySql database) that is one of the stages already completed. http://www.lullabot.com/articles/drupal-data-imports-migrate-and-table-w...

I just moved my production site to a new server on a new host, and the process is actually very easy. Just make sure that the new host has decent import file size with regards to the database. My new host had a max of 50MB for importing a database and my database was 30MB, although my old host limited me to a 2MB upload. Would of had to import through the command line with the old host instead of phpMyadmin.

On your new host upload your files, pay attention to any .htacess files and the settings.php file as these will most likely need to be modified.
The links corresponding to your domain name will have to be fixed if they are hardcoded anywhere if there are any changes to any urls, if they're relative then it will be much easier to avoid strange issues.

Create a new empty database, and import your existing database into. Change your settings.php to reflect the new database, and any base URL changes. Look at your .htaccess file to make sure it conforms to the requirements of the hosting account. Trial and error may be required but these changes take effect immediately so it's still a quick fix

Taking the time to get demo site set up the way you want before is the smart way of doing this, then the move to the production site should be really simple.

Mine process was fairly quick...

1. Put site into maintenance mode, turned off clean urls, and cleared all caches + downloaded all site files to my work PC
2. Exported the database twice, once compressed and once un-compressed, just to be safe
3. Uploaded all site files to new server, changed .htaccess + settings.php
4. Imported database.
5. logged in and checked for missing files and broken links, permissions etc..
6. put site back into on-line mode
7. checked links and functions as BOTH anon user and auth user to make sure things work for everyone
8. checked db-logs and error reporting to see if i missed anything

Although I did have some downtime due to the DNS propagation, my new host provides temp access and I use OPEN-DNS so I was back on my full site in under 2 hours. Customers still had to wait for their ISPs, though a well devised site off line page answered any questions and gave them contact info to address their needs while the site moved. Got 2 sales over the phone during the downtime.
feel free to ask any questions if you need, I'll try my best to help.