This sketch is a compilation of the FastLED Color Palette and a button press. There are a bunch of mode options to choose from within the sketch, including adjusting the speed and steps of the preset palettes and creating your own palettes and modes.
Depending on the choices and number of LEDs, you may be able to fit 8-10 of these modes on an attiny85 board like the Trinket or Gemma. Larger capacity boards will be able to handle more.