Bloop Slate

Hi all, im just trying to work out if the arduino is the right platform for my next project.

What I want to build is a bloop slate; which is used when recording video and sound separately to help sync the two back up later. It works in the same way a traditional clapperboard or slate works but is smaller and a more convenient on faster moving documentary shoots.

This is what a commercial device looks like but they aren't being made anymore...

This is what I would like it to do;
Its basically a small box with a button on the top and a 3 digit 7 seg LED display.
When a momentary button is pressed the numbers disappear for half a second and flash for 1/25th of a second, simultaneously a 1khz tone will bleep (on a speaker or buzzer) for the same amount of time. The numbers would reappear after about another 2 seconds, incremented by one digit ready to mark the next take.
There would also be a reset button to bring the numbers back to 000

While I'm pretty good with electronics my programming isn't great and have been considering using the 4026 counter/display IC but thought may using an arduino might be a neater and more flexible way to do it.
I've found the counter, tone generator and display details in the playground but not entirely sure how to put all the code together!