which Arduino product would work the best when controlling about 100 - 200(max) LEDs?
If you mean RGB LEDs then multiply this number by three as each RGB LED looks like three LEDs
You need external hardware with this and so any arduino will do. Use this code:-
http://www.elcojacobs.com/shiftpwm/
This is for low power LEDs, doing it with power LEDs is a whole other board game and several orders of magnitude more expensive.