In SharePoint 2013, adding selected webparts to a page dynamically

I have been given an interesting problem to solve. We have a publishing site in SharePoint 2013. Requirement:

1. Every user should able to customize their home page with ease.
2. Load available webpart initially.The design having 4 web-parts zones organised in a 2 by 2 fashion (2 web-parts by 2 web-parts)
3. Provide a hyperlink "Customize this page".
4. Onclick should display all available webpart in a popup with checkboxes.
5. User can select/unselect his interested webparts.
6. Checked webparts should be visible in home page.
7. User should also able to move webparts.

I would really appreciate any help or advice on this.