If you're selling anything from your website, or collecting information from site visitors, you will want to make sure you have secure server options available. Depending on your needs, you may be collecting credit card information or other information of a personal and private nature. For example, you might want to collect information from website visitors like their names, home mailing addresses, and birth dates, so that you can send out birthday cards with special discount coupons or gifts on their birthdays.
If you have a database element to your website including things like inventory and catalog information, or message forums, you might be more concerned with finding a website hosting company that performs regular backups of the data on your website for you, just in case anything were to happen to the server where your information is stored. It's a good practice for you to be keeping at least two separate copies of your website just in case you need to restore the website at any time, but for people who have more than online informational brochure type websites, it may be worth the expense to have an automatic backup routine in place.
Keeping backups is also crucial if you ever decide to change from one website hosting service company to another. If you don't keep backup copies of your website, you might have a very difficult time getting the files that make up your website from the hosting company if they go out of business, for instance.
3. Database access
If you're going to have a need for databases on your website--for things like forums or inventory or catalogs, for instance--you'll want to make sure that you have the appropriate software and options available to you through your website hosting company. Many databases use MySQL databases, and these are often included standard with many website hosting service packages. The number of databases is limited, so you will want to be sure that you purchase enough for your particular needs.