We're presently searching for another webhost. The organization should offer Linux based hosting and support WordPress and Drupal based websites.
Besides good prices and tech support team, the webhost must have the most recent stable versions of MySQL/PHP, and provide modern management/support tools (i.e. cPanel, Fantastico).
Drupal-only hosting is better with Acquia.
Apart from that, there's the official list: http://drupal.org/hosting
P.S. I'm not a WordPress expert but Drupal has more technical needs in comparison to WordPress therefore it is safe, IMO, to express that Drupal hosting would suffice WordPress.
I have been happy with WiredTree for nearly 2 yrs. Good support, always up, and pretty reasonable prices.
I personally use dreamhost and pretty pleased with it.
"I believe this may well be a little more appropriate for superuser.com" - except this is not really an issue could it be? It is simply an argument of intent. We're searching for x, which are the qualities it will have...
Fine, but exactly what do you anticipate me to complete about this?
For Drupal, you should use DrupalGardens that provides Drupal as PaaS, so less setup hassle.
I've been using media temple for just two years. I am very pleased with the service, support. It's might be not the least expensive but it's worthwhile. Oh and that we really are a drupal shop.