Website redevelopment project in Wordpress

General information for the website: Admissions site for a school
Description of every page/module: The site is relatively basic with 6 key pages below with sub pages for more detailed content.
Home
About
Admissions
ABA
Therapy
Contact
Description of requirements/features: The site needs to look more modern with full screen display, be Responsive for mobile users.
Needs to incorporate existing social media links and feeds.
Needs to include a trackable contact from so the number of enquiries can be monitored.
Need to include a way of having buttons / widgets on certain pages.
Needs to have sub menus on certain pages.
Extra notes: Site be enhanced is:
http://jigsawadmissions.co.uk/

Needs to look more like a combination of:
http://careersatjigsaw.co.uk/
and
http://jigsawplus.co.uk/

We like the look and feel of the careers site. We like the simplicity of the jigsaw plus site.

Good bits to replicate - Top menu bar and colour scheme of the Careers site.
The shaded components on the home page.

Needs to have the option to add widgets / button to pages. As in the existing Admissions site.

Needs to have a sub menu system for certain pages - similar to the menu on the this page: http://www.surreycentreforeatingdisorders.com/our-services/

Test site is set up and ready to go.