One of the interesting things about Media Temple is the breadth of hosting solutions they offer.
Among their least expensive plans is WordPress-specific hosting. Just $20/month, but very powerful and fast hosting, thanks to it being tuned just for WordPress. WP-CLI is installed right on it and it auto-updates WordPress core for you. Not to mention it's all on SSD's, you get SSH access, and you get 24/7 WordPress-certified support.
There are loads of plans that scale up from here, all the way up to incredibly high-end servers. I was just chatting with some Media Temple folks about some real white-glove support they were doing with a huge enterprise client. Guess what kind of site it was? WordPress. All set up on Amazon Web Services and fully managed by Media Temple.
If you go for Grid or DV (level 1 or 2), make sure to use the code CSSTRICKS to save 20% the whole first year.