I’m on Hover. They’ll host and email inbox for you, but not a website.

Not quite sure what you’re looking for, but I think Dreamhost can just hand you an Ubuntu box you can SSH or SFTP to to manage your site.

Check what your testing organization is using first. We’re using Selenium at work, except for one small team that used Cypress because they couldn’t be bothered to find out what the test of us were using, so now that team is faced with either maintaining their own version of the CI pipeline and their own tooling (and not having anyone to ask for advice) or rewriting all of their tests. Not an enjoyable choice to have to make.