Q: What are your hosting server's hardware specs? The server hardware is very important as the faster the server is the faster your site will be, especially when your site is using dynamic content created by server side scripts/application which usually interacts with a database. Most of these are mentioned on the webhost site, most probably under their FAQ section. If you are not computer literate it is hard to tell if a web hosting server is fast enough. However you can always take a look at the server specs or at least compare the servers of two webhosts to see which one uses more powerful and faster machines. Q: How many sites are hosted on a single hosting server? The number of sites hosted on a hosting server will tell you how much the servers are loaded and if your webhost is overselling space and bandwidth. There are quite powerful servers that can host up to several hundreds sites without a problem. Q: Do you have backup/spare servers? Most web hosting companies always keep spare servers on-line. So, if anything happens to the production server where your account is hosted they can bring up a spare server and restore your site from the latest backup they have. So here comes the next question :) Q: How often do you make backups and where are these backups stored. Do you have off-site backups? Web hosting companies usually offer daily and weekly backups. Some of them store the backups on a separate server - always recommended, while other keep the backup of your site files on the same server. In such a case if the hard disk of the server gets busted the backups are gone too. So a backup on a separate server or a tape backup is always recommended. Some web hosting companies even offer off-site tape backups. It is up to you to decide which one you will prefer. It is always a matter of how important the information on your site is. For example if you run an on-line shop on your site, daily backups are the better solution as they reduce the risk of losing orders and other important information. If your site is just static HTML personal or company site with some general information that does not get updated all the time, weekly backups are more than enough.
I would advice to add more questions about the type of expected treatment you want from the web host, i.e. is my support request always attended by the same person, and he/she will not pass my request around different technical staff ? etc. you must first understand what type of support you really want from your web host, and then put them all in questions, this will help you get a web host that fits you.