Media Temple is the host we both use and recommend here on CSS-Tricks.
Hot off the presses: Media Temple has launched Enterprise WordPress Hosting. This is for large-scale WordPress sites that need the scaling and high-availability of AWS, all managed by the crack engineers at Media Temple.
A little behind the scenes: everything is built on Docker containers. When a high traffic event happens that requires scaling up, that happens in seconds. Media is uploaded and stored on S3, then delivered through CloudFront CDN.
This is some hardcore WordPress hosting, with all the support you need. Remember to use code CSSTRICKS to save 20% for the first year.
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Sponsor: Enterprise WordPress on Media Temple is a post from CSS-Tricks