Upgrading Servers, Apache, PHP, MySQL w/ Drupal 4.7.x

I'm going to move several Drupal 4.7.3 installations from my current shared host account, running Apache 1.0.33 (I think), PHP 4.4.1, and MySQL 4.0.27, to a VPS with a new hosting company. The new server is currently running Apache 2.0, PHP 4.4.2, and MySQL 5.0.22. I'm considering upgrading the PHP to Release 5.someting, too.

My question is: How do I perform such a move?

Or, will this approach work:

• Install Drupal 4.7.4 as a new application on the new host using the appropriate files for the new versions of PHP and MySQL.
• Install the same modules and themes as I'm currently using.
• Unload/copy the MySQL databases from the old host and upload them to the new host. If I can't do this with the entire database which tables can I copy.
• Copy associated files, e.g., images, to the new host.

Any and all help will be greatly appreciated.

Mel