Justin has given an excellent response. You may find my story of interest.
I've had my own Moodle site since 2003. I teach English as a foreign language in a public school and college. I use Moodle for blended learning (face-to-face and online) and now blended online learning (WizIQ plugin and Moodle). I can't see teaching without Moodle and technology. Justin's PoodLL is the highlight of all of my Moodle courses.
I have gone from shared hosting to dedicated servers. Not all dedicated servers cater to Moodle so I had to change twice (migration is costly). You need to make sure that they the dedicated server caters to Moodle. The worst part is that if you want a dedicated server that is compatible with Moodle, you may not get any support for Moodle. You will have to manage your server and your Moodle installations (upgrades and plugins). That's a lot of know-how. Moodle partners hire people, who have the know-how, but that makes their services very expensive for some public and private learning institutions and for individual teachers.
I'm just a teacher who cannot work without Moodle. I love teaching with Moodle. How do I manage because I cannot afford even the cheapest Moodle partner pack? I have my own dedicated servers because I have a few Moodle sites, someone who manages the servers, and Moodle experts.