Hello.
I'm assuming the plan that would most suit you would be a linux shared hosting plan.
The linux shared hosting plans can be seen here:
http://www.eukhost.com/cpanel-web-hosting.php
eUKhost provide a free domain with each of the shared hosting plans for linux, so you can either transfer your domain over to eUKhost for free, or keep it with your current domain registrar and point the nameservers to the eUKhost nameservers.
PhpMyAdmin is provided with all linux shared hosting plans, so you'll be able to manage your databases etc.
Let me know if you need any more help...
