Some of my older collecting buddies SWEAR by Armor All, but I'm not a fan of it. (I've seen the effects of it years later, making various vintage materials sticky, tacky, slimy, and even breaking down surfaces in some instances.)
For Atari stuff, the shell can be soaked (toothbrush & soap are GREAT for those grooves) and the paddles & sticks can be taken apart and soaked, as well. With a bit of elbow grease you can have it all SHINING.
Have fun!
Fun fact: Back in the late 70s, my older brother discovered that you can replace the red joystick button with a common ChapStick cap!