New Tab King does the most visited sites and a whole lot more. I believe you can also click on the arrow in the address bar to get the most visited without any addons.
I know there is one for doing exactly what you want with 4. but I can't remember the name of it. You could configure the shortcut yourself. This appears to do it by right click if that is any help.
Some other add-ons are: New Tab King & Speed Dial.
I must say that Super Start looks pretty good though.
No feature like that is built into Firefox.
Look for an add-on:
https://addons.mozilla.org/en-US/firefox/search/?q=new+Tab
https://addons.mozilla.org/en-US/firefox/addon/new-tab-king/
Has a number of "themes" that appear to used Favicon-like images, but that extension mat be at EOL as its domain name seems to be available.
Support forum is here: https://newtabking.uservoice.com/forums/31779-new-tab-king-forum