Hosting location, HTTP2 protocol support, HTTPS support and free SSL certificate support, a backup system, storage capability and PHP version support are some of the important factors when deciding which web hosting to choose.
Here's some factors for you to consider when looking at hosting:
Location - should be as close to the bulk of your visitors as possible
HTTP2 protocol support - this protocol speeds up the download of files from the web server to visitors. It was released in 2015 and many cheap hosting providers still don't support it.
HTTPS and free SSL certificates - on the modern web you really must run your site in HTTPS encrypted mode for speed, security and website conversion. There are still some hosts who want to charge for SSL certificates. Top tier hosts have free SSL certificates built in
PHP version - PHP is the programming language WordPress runs on and your host should support the latest version. Each version is typically faster than the last one so running the hosting with the highest version the site, theme and plugins can support will be best for speed
Backups - you want *some* sort of backup system albeit we recommend you run your own backups outside of what the hosting platform provides.
Email hosting - do you need email hosting? Many providers don't provide email hosting as there are a large number of dedicated cloud email hosting providers that do it much better and cheaper, eg Microsoft's Office 365 suite and Google Gsuite (aka business Gmail)
Staging area - this is becoming a must have for WordPress hosting so changes and updates can be tested before going live
Support - what is your support expectation? 24/7 phone or will business hours live chat support suffice?