Hi Mike!
Thanks for getting in touch with us. Let me help you with this topic.
We don’t really have any specific recommendations for a hosting provider. However, If you are looking to improve your site’s performance then let me point you to the following article about Performance Considerations you should know about.
After that, if you decide to implement a caching system then you can move to these articles: Caching: What, when and how and Caching month view HTML in transients
Finally, there is a good article George put up here that groups a set of developer plugins. It’s a bit more technical than the others but will definitely be of help if you are into development.
I hope that helps. Let me know if any follow up questions.
Best,
Victor