I need a currently existing website to be rebuilt from the ground up

General information for the website: Holiday property listings and blog
Kind of development: New website from scratch
Description of requirements/features: I am looking to build a holiday property listing website that also has a high traffic blog and an events section.
There is an existing website which will be entirely replaced with this new site.

It is currently built using wordpress but it is a very inefficient site and needs replacing with something lean and fast.
So first of all i DO NOT wish to use wordpress for the new site. Wordpress is not an option.

I am open to suggestions on what CMS would suit the project best but i have some very exacting requirements.

ONE:
The server the site will run on is Linux. This will not change so this obviously affects what CMS' can be used.

TWO:
The CMS must be FAST! I want this to be as efficient as is possible. I had considered the Statamic CMS purely because of its speed (and nice interface) and also Craft CMS (again, faster than wordpress and the interface is a joy!)

THREE:
The interface must be clean and easy to use (again, Statamic and Craft are good examples). This rules out Drupal, Wordpress...
I want the admin area to be focused and not have all the extraneous odds and ends that systems like Drupal or ModX have.
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