One of the first things to keep in mind is choose a web host that offers 24/7 service. I have worked in this industry for 13+ years, and problems rarely happen during standard business hours. So, when I look for a new host I check out what their support options are first!
Next, if you choose WordPress as your platform then an SSL is important and is often included in a good hosting plan. If you want to be hands off on backups and security – choose a company that offers those features to protect your data from loss and hackers.
I love WPEngine personally (yes, they include all of the above and more). Their close relationship with Genesis (which I have been using for 9+ years) makes me trust them all the more. You can check their plans out here and this link offers you 3 months free with an annual plan.
**The above does include an affiliate link. I do get a commission or benefit if you choose to purchase through the link. This said, I only recommend products I use myself and trust implicitly.