Don't use GIMP because it only has very basic vector capabilities. GIMP is a raster image editor. It's not the right kind of software.
The whole thing can be made in Inkscape. You can import your jpeg as a guide to redraw it. Delete the jpeg afterwards.
Enable the page grid and snapping to grid to make the following steps easier. I assume basic familiarity ...
There's no need to use a modifier key to do this in GIMP.
After clicking and dragging a curve, release the mouse button, then click and drag the Bézier handle to a new position, then continue with the tool.
If you want to fully retract a Bézier handle, you can Ctrl+Shift+click on it
Closing a path is achieved by Ctrl+clicking the first node ...
It is creating additional width markers. When markers are close to each other you get sharp, drastic, changes in the width.
In CS6 you have to be very careful about where you click and wait for a marker to highlight before you click. It's very "buggy" and inaccurate in CS6 (at least the Mac version is).
Often you see the highlight when the cursor ...
On a related note, if you want to move points around and you don't need curves, there's a checkbox in the Path tool options called Polygonal which allows you to quickly move around path anchors and ignore handles all together.