There are a lot of guides how to get started with arduino. I just wanted to list some Hardware which you can use.
Plug and Play Solution, just plug in the USB cable and you are good to go.
– genuine arduino 20€ / 26$ click
– clone 8.5€ / 11$ click
– Nano 6€ / 8$ click
– Expansion shield for the Nano 5.5€ / 7$ click
Programming with an USB -> Serial adapter (FTDI)
if you want to program the Pro mini over USB you will need an Serial adapter
– Pro mini 2€ / 2.5$ click
– FTDI Programmer 3€ / 4$ click
There are also Nano boards with a CH340G instead of the FTDI chip. Those are cheaper 3€ / 4$ but i haven’t used these yet.