I will test :
The site as an regular user
The speed of the site;
any errors (404 500 , etc.)
The HTTP response headers
Login Portal (if you have it, I will create an account)
I will also check if your site supports SPDY and if it can be pass the validation with the W3 validator.
WARNING:I'll test only 3 pages.
Your site should be in English or in Spanish or in Portuguese.