How to pause & continue led sequence with button press

I think you could use any Arduino board, including UNO like @anantmohit already said.

I don't know if the fact you're saying you're "new here" means you have some kinda experience with Arduino and/or programming. If you don't have such experience I think you need to start learning a bit about Arduino before, together with at least a basic knowledge of digital electronics (limited to pushbuttons and LEDs just for now) and the C programming language.

If you already know enough about that, my personal advice is to use a simulator like Wokwi, so you can just test the wirings (you can draw your circuit with an Arduino and all the other elements needed) and the code without even buying the hardware. when the simulation looks good to you, you can start putting your hands on the real hardware to build a prototype.