There are so many factors that go into this, and things you might get confused with, so I'm going to make this as simple as possible for those of you just starting out.
One thing you should realize is that most web hosting providers are going to be relatively similar with the same features at the bottom level.
But, this is what they want to look for in a good hosting company:
- Safety: Website security is important, you don't want to be hacked, and if you have some clients, you certainly don't want their information to be hacked. So keep in mind what kind of security features are offered.
- SSL certificates: At Google we make sure that sites are safe today, especially if you are collecting personal data or credit card information. SSL certificates help encrypt data; you can tell if they are there when you see https in the url (like this one). If you have an ecommerce store, this is non-negotiable, and these days since Google places an emphasis on secure sites, it's best to set it up from scratch.
- The cost: A shared hosting account should be quite affordable, certainly under $ 20 a month max, while VPS and dedicated hosting will cost more.
- Backups: It's very important to back up your site regularly, so make sure your hosting provider gives you backup options.
- Customer Service: When you start building a site, you are going to have problems, so it is very important that you choose a hosting service that has good customer service to help you get out of the problems that (most likely) you are going to to put.
- The email: You want to have a professional email address that is from the same domain as your URL. So make sure your hosting provider also gives you the opportunity to add email.
- Reliability: You don't want your site to go down, ever. That means it's important to work with a hosting company that is reliable and keeps downtime to a minimum.
Your natural inclination is going to be to go with the value option, something that is affordable, but has some good features and offers a lot of customer service.