Some key features to look for in a web host include:
Fast Time to First Byte (the time it takes for the web server to deliver the first byte of data in a request)
Free SSL certificates that automatically renew
Focus on security and performance so that an attack or spike in traffic on another unrelated site on the same server will not adversely affect your site
Included Content Delivery Network (CDN) to duplicate your content closer to the geographical location of your visitors for faster content delivery
High availability (typically 99.99% uptime) so that you have as little downtime as possible
Backup and restore capabilities, preferably included at no additional cost
Maintenance package if your site uses a content management service like WordPress
Easy access to support via chat, email, and phone in case of problems or questions