Using SharePoint Designer you can create multiple zones in a page layout.
Just Create a Page with any layout.
Create an HTML Prototype like below:
<tr><td> Your 1st new webpart zone here </td></tr>
<tr><td> Your 2nd new webpart zone here </td></tr>
<tr><td> Your 3rd new webpart zone here </td></tr>
Copy layouts fro the page you created and put them in the above
make sure you keep distinct Title and ID for the zones. Paste this table in your above custom page.
To add an image and description of the site and add few links to the document libraries or SPLists you have multiple webparts already available if anything remaining you can achieve in CEWB (Content Editor WebPart).
You can apply branding also as you want. Add reference to your css file and js file.