The Emacs start up page has image, link, and fonts with different size all in one. How can I create a page like that?
Emacs doesn't come with a mode that can create all those effects (although you can get some of them with Enriched mode). You'd have to write Lisp code to create the page you want.
The actual startup page is created by the function
fancy-startup-screen in the file
startup.el. You can look at that to see how it does what it does. You'll probably want to read the Emacs Display chapter of the Emacs Lisp Reference Manual.
Note: You can display the startup screen at any time by typing
M-: (fancy-startup-screen) <ENTER>. (You can't use
M-x because it's not marked as an interactive function.) There's also an "About" screen that is very similar, which can be displayed with "Help > About Emacs" in the menu bar or
C-h C-a or
M-x display-about-screen. (
fancy-about-screen is the function that actually creates that screen.)