I would recommend you don't use GIMP for work like this. It's just not the right tool for the job. Use a vector image editor instead.

Inkscape's Bézier tool works very similar to the Bézier game, but the functionality of the Shift, Alt, and Ctrl keys is different.

 - Holding down Shift, creates a corner point and allows you to drag out
   a curve handle
 - Holding down Ctrl, snaps lines to angles of multiples of 15°
 - Alt does nothing

You only really need two nodes to form an S shape.  If the S shape is more complex you can use more if you want. There are no rules. Do as you please.

Example of a two node S-shaped curve.

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/e1LoH.gif