I've used the keyboard and mouse for years for flying and works wonders just by changing the yaw and pitch and sensitivity to the point of one little motion moves the plane quickly in one direction but takes practice and I have beaten joystick pilots too so it works but practice makes perfect.
Honestly any of the gaming headsets work but try to get one with really good surround sound and check out some reviews on them before buying any. I myself just recently started using a headset and realize the difference in sound quality and being able to hear far more then I used to with speakers.
You won't get any good joysticks for the price range your looking at so if you want to stay below that limit go to your nearest best buy and buy the one below 75$ otherwise your going to have to up your budget range if you want more durable and better sensor on the joystick.