As far as games that use joystick, I tend to mostly play Donkey Kong, Ms Pac-Man, Defender, Dig Dug, Street Fighter Alpha 3, 1942 series, R-Type, Rastan, Strider, King of Fighters series, Metal Slug series, Robotron, Smash TV, etc, etc
As for the perfect stick, the U360 is staring you dead in the face. It's as close as you're going to get.