Hockey Shot Speed Leaderboard System

I created a project to test the speed of a hockey shot and I want to implement a new feature, a leaderboard system. Whenever the project boots up, I want to print the top 3 fastest shots ever recorded on the system.

From my knowledge, the arduino has an built-in hard drive that can store small amounts of updating information permanently on the board. This can be done using the EEPROM library. I would like advice on how to go about adding this feature. My idea was to compare the previous shot speed with the most recent shot speed, and the shot that is faster will be added to the top of the leaderboard. This process continues with the leaderboard shot speed being compared with the most recent shot speed, and the leaderboard being updated accordingly. Any suggestions on how I can begin writing the code?