I use Unlimited http://www.unlimitedwebhosting.co.uk/index.php
If you can port your existing site then as Deano says get a copy ande stick it in your new host.
I think you have built the site in Webs proprietary language, this may cause problems, if anything goes wrong or you need to update.
We build a lot in Wordpress, its free, open source and stable. There are loads of template sites to choose from have a look.http://wordpress.com/
Good tutorials and good support.
Joomla and Drupal are also great to develop with.
Hope this helps,