Yeeeeh! Amiga's rock I had an A1200 and a CDTV.
I've still got boxed copies of Golden Axe and Alien Breed just incase I ever bought another. Get a copy of IK+ (kick the bombs!) and Skidmarkz, wicked little racing game you can even tow caravans and use them to wiplash you around corners while racing a cow (you'll see).
Back in the day I used to create drum + bass tracks in Protrakker (4 track sequencer with samples in sterio wooohooo)
The black box you plug into the TV is the TV modulator (built into the A1200), as it's been said there is a PSU + RF (ariel) cable needed.
Zipstick joysticks is where it's at but megadrive joypads will work also.