What template to use for building a site in form of algorithm answers

HI the Hive

Very much new to site creating. I am planning to build a site which home page would have 2 main questions: for example "red" or "blue"? Each button would lead to the next page for instance, "free" or "out of pocket fee" and so on. When all questions answered, the visitor will be given the list of final options. 

So I have 3 questions:

1 What template to chose?

2 What is the name of this algorithmic approach to the site building?

3 Any plugin to use to sort all possible options as per visitors answers? (blue--->free---->square---->local :  Theodore Roosevelt at www.TheodoreRoosevelt.com) 

Many thanks in advance

Alex