project direction and fesability

Hello, I am new to the arduino system and I have a project idea I wish to persue. It is a reaction training system using large led arcade type buttons that light up, get pressed, turn off, and then an alternate button lights up and so on. Perhaps with an lcd display that records time and accuracy. Similar example would be the cardiowall, t-wall, reacta, batak, and fitlight systems that are on the market. My question is; is this possible and which kit would be best suited. Thanks.

Uno, buttons, LEDs & current limit resistors, and LCD with serial, SPI, or I2C interface:

May need buffers to drive the LEDs, depending on what is selected for "large led arcade type buttons".
Some examples:

The LED and the button are usually on separate sets of pins.

This is the second such project we have seen here in a week. Is this some sort of class assignment?

Sounds like a typical wacamole project. It's not only possible it's very basic entry level type stuff.