Searching for a new web host.

Are there any specific questions I can ask that will help determine who to use?

There are several questions that you can ask any potential hosting company you are looking at. Here is a short list that will get you started.
What sort of physical connection does the web host have to the Internet?
What server hardware and software does the web host use?
How much disk space does the web host guarantee?
The biggest issue you may find is how easily they are reached by phone. If you cannot reach a hosting company by phone 24/7, then you should continue your search elsewhere.
The Surgeon's Advisor Team