Initial approach to developing a web application

When I want to make a web application, what should be the initial approach to implementing the website given I already know the wireframe?

Here I am specifically asking whether:

1. I should design the whole layout first then implement functionality one by one, Eg. I design the homepage exactly as it is on the wireframe/sketch without implementing any functionality such as routes/login/posting

or

2. I should implement functionality as I go Eg. I am making the homepage starting off with the nav-bar. There are navigation links, drop-down menus on it and I apply routes/scopes to the web application immediately.

Maybe there is a better approach and I am curious to knowing what would be the benefit of taking up certain approach.