Custom Wordpress Homepage

I would like to create a Widget Box based custom homepage for a wordpress site. The custom page can be added to a basic Wordpress 2012 Theme and appear as the set home page. The design is a three column design with a logo header, then a menu with submenus, then a slider covering the first 2 columns and then all boxes after that. I've created a sample layout in Excel that should make the concept much clearer. In each widget box, I should be able to have text, links and a list of the newest posts from a category (with the number of posts variable for each widget). The style elements of the widgets should be laid out clearly in a stylesheet I can adjust as I want for whatever final colors/fonts etc. I decide to go with. The headers of each widget box should be able to link to a URL I set for the box. The page should be mobile friendly so that each widget width adjusts to the screen width and reformats into a single column. I should be able to choose the order of widgets in each column for standard layout (example column 1, box 4) by adding numbers or using a drag/drop layout as well as choose order for mobile layout (example, column 3, box 1) may show up as the fourth box in line in a single column mobile display. Any questions let me know.