Since I had used Inkscape and GIMP to some degree in the past, I spent most of my time getting familiar with FreeCAD.
I opened up FreeCAD and tried to replicate what Neil had shown in class. This was not successful; there was quite a bit of implicit knowledge that turned out to be hard to figure out just by clicking around.
I then found a pretty good FreeCAD tutorial, and worked through that for several hours.
Side note: FreeCAD crashed with segfaults a couple of times until I exported the proper language environment variables, which fixed things for me. I've since added the following lines to my .bashrc file:
export LC_ALL="C"
export SESSION_MANAGER=""
The tutorial was this FreeCad Tutorial on Creating a Simple Part with PartDesign. With this, I got a decent understanding of a few of the different workbenches, and of how to apply constraints.
By the time I was done, I had this lovely little part:
It was clear to me that I had a ways to go before I'd be able to design anything large, complex, or useful, but it's good to start somewhere.
As far as final project ideas go, I've been thinking about making a CNC airbrush, capable of working in a really large scale way. One idea is to have the x axis be on wheels, so that you can just use it on the floor rather than needing an explicit bed. This means that the X dimension would be more or less unlimited, which I like the sound of.
I'm guessing that having the X axis be on wheels might induce some issues around accumulated error, since little tracks or simliar do a nice job of keeping everything strongly registred. I could imagine solutions here including little laser-based distance measuring devices, or maybe just setting up an additional guide wire or chain that the machine pulls along to stay registered. Anyway, here's a little sketch, suitably down-sized for sharing.
Ah, wait, why do I want a massive scale CNC airbrush? Good question. The basic reason is that I want to make big paintings.
(Q. What is good art? A. Big art.)
Really. Big. Paintings.