Recommended hosting companies for best TTFB?

[RosemaryB]

Right now my client has a wordpress website with over 300 pages (mostly blog posts).  Their average TTFB (time to first byte) is 3017 ms.  They have a SSL and their current hosting company is Site 5.

Does anybody have any recommendations for a better hosting company?  We are willing to up the budget for better performance.

[LesleyPaone]

Do you know what kind of account your client has? Is it a shared / vps / or ededicated machine they are using? Also, is their site primarily static? Or does it update constantly or have interactive updating features like an e-commerce site.