The first thing he told me to look for is: "Customer service" - A web host who has a team available 24 hours a day is one that you can count on. If that wasn't good enough, here is what happened to me. I got my hosting account all set-up. Start building my site, and then needed to create a temporary ftp login. Did all that, got the tech to fix some issues I had and then I went to delete that temp login. I hit the wrong button and my site was wiped out. Gone!
First set up your web hosting account with the your provider. It will make things easier later. Some providers will not allow you to initially set up an account when the domain is already associated with another provider or account. I underline the world 'initially' as this applies only to a brand new account. This is the case for Bluehost anyways. The workaround for this is to simply get a new domain. Some hosting providers will offer a free domain with new accounts so you can use this opportunity to register a new domain and then use that domain to set up the account. The reason for this is that when you first set up an account they will use the domain name get more info as the account name. Every other domain is considered an 'add-on domain'.
The next feature that he mentioned is: Reliability - You need a host who you can trust. Don't go with no web host who hasn't been around for more than five years. Many new web hosting providers don't have their own servers. They share a service Hostinger with other companies. So they rely on that company to restore their problem for the. The longer a company been around the bigger the chance that they have their own servers.
If you are transferring to a new web hosting provider then you would need to change the DNS settings. There is a way to receive and send email in the midst of the transfer if you set up additional MX servers but let's leave that for another day of discussion. For now, however, we're assuming that you've already changed your DNS settings or your are only simply transferring to another hosting account with the same provider. All the step-by-step images are specifically for the control panel CPanel. If you are using Plesk or some other control panel Webmin then please contact your web hosting provider's tech support team. They should be able to guide you.
If price is an issue then find a list of companies and compare their prices and features. You can find websites that do exactly that. Just search for the term "top web hosting providers". Also there are many companies offering a free domain with the hosting account. Make sure you learn all the companies offers and discounts.
This is normally not an issue as all the features are being displayed on the website before you sign up for a plan. However, you need to know what you need. For example: you are going to install a third-party web application, so you have to find out whether the server can support such web application or web hosting provider allows you to do so.