Build a Website and migrate data from an existing one

We are looking to develop a website quickly from an existing theme. The main requirement is that the website should be SEO friendly, responsive and fast-loading<2.5 secs. Here are some of the features we need: 1) magazine style home page encouraging social engagement . 2) blog posts should have social sharing icons and allow for comments 3) capability to add other pages 4) users should be able to login via Facebook or email. Once logged in, they can upload a profile pic, add few details about themselves, comment, ask questions and answer questions. Answers can be voted upon by other users. Asking questions would cost some credits, and answering questions and being uprooted would increase credits. Some users can be promoted as authors depending on number of votes or based on admin choice. Some users would be experts on a category based on admin choice 5) allow people to register for events 6) an ecommerce shop selling digital products like books and services. Some of our products have video tutorials and hence, we'd like to be able to show those 7) contact page 8)pop-up asking users to join if they have been browsing for sometime but aren't signed in 9) Search functionality so that posts with certain tags get priority (we've done this previously using relevanssi search, we can share the code with you) Additional plugins - iThemes Security, SNAP auto poster, Updrafts Plus back up, mail chimp, relevanssi search premium, Yoast SEO Other things: We are on a tight schedule. We have the logo and palette colors etc and we aren't too fussy about the design. We want to pick an existing theme and then customize it to suit our needs. The faster we can do this, the better.