Ramzey nailed it.
In setup, controls, joystick, settings.
You'll have 2 blue boxes on the right side, a page of sliders on the left.
First adjust deadband. This tells the computer how much center "slop" the joystick has. If your stick is new it won't need much deadband. Older sticks need more. You'll need to set it for both Roll & Pitch.
If you can pick up the base, and gently wiggle the stick and see curves/lines in the top blue window. You need to increase deadband. Or if you use a single finger on the top of the stick. Gently swirl it so that it just bumps the springs. Again, if you see curves/spikes increase deadband.
For the "don't move controls so rapidly" problem.
First you need to find out which axis is the problem. Up down (pitch) side to side (roll) or Rudder.
Gently move your control side to side, start small. You should see smooth curves. If you get a spike, thats your problem. Add a bit of damping to that axis. Then try again. Check for all 3 axis to find & cure the problem.
Last while your here if you have a "twisty" handle. You probably are kicking rudder in while turning. Setting deadband "big" on the rudder means you have to twist a bit more before it actually starts inputting rudder. You'll do it less often by accident.