While I was researching, I found out new terms such as LED driver and PMW and I don't really understand what they mean?
http://www.thebox.myzen.co.uk/Tutorial/PWM.html
Driver means the circuit between the LED and Arduino output pin that amplifies the voltage and / or current of the output pin to match the LED's requirement.
which type of LED strip should I use?
Depends on exactly what you want to do:-
turning them off/on, flickering, or changing colors.
Is a bit of a hand waving explanation.
I know there are 2 types of LED strips
If only this were true, their are lots of different types. The main divider is do you want to change the colours and state of each LED individually or do you want the strip to show all the same colour / brightness at the same time?