I use a CyborgX joystick. Its quite solid, folds, is adjustable and has served me well for about two years now. It was about £35 if I remember correctly ($55.69 ish). Slightly higher than your requested budget but it stood up to my dad trying to fly a plane with it (Basically he tried to show-off on x-plane, lost altitude, tried to pull up by attempting to push the joystick beyond its normal limits).