For normal counting,
Pin 13 should be low (Enable)
Pin 15 Should also be low (Reset)
Rising edge of clock is required to increment the counter i.e at pin 14.
"Can I use a switch setup as shown in the flash animation for the clock input or do I need a 555 for it? "
You can use a switch if you run it through a debouncer first. Otherwise the counter will probably increment several counts each time you close the switch. Here is a good explanation of contact debouncers. Do a Google search if you want more ideas. There are many ways to debounce a switch.