My first game system would be the Amiga 500. I don't really have a favourite, but I can tell you my favourite characteristics/games about each game system.
PC: fully upgradeable to run games at max graphic settings, uses mouse and keyboard for precision and flexible button configuration.
PS3: Blu Ray player, some great exclusives such as Metal Gear, Gran Turismo and Uncharted, can't wait for 3rd game.
Wii: Cheap and Cheerful, great for parties. Warioware works well.
PS2: DVD player included, first console to have GTA3, which is still a great game to play. Metal Gear series and Final Fantasy exclusives.
Xbox: First console with a built in hard drive
N64: Mario Kart 64! Re-introduced analogue joystick control and Z-Trigger
SNES: Again... Mario Kart, Donkey Kong Country (one of the earlier games to use pre-rendered backgrounds), Super Mario World.