Hey Rory,
There is indeed free software you can use to design patches for the embrodery machines. It’s called InkStitch and its an add-on for InkScape (also free!). The software will give you a really good visualiation of what your design will look so that’s probably a better guide for detail than my best guess but I think you might be OK looking at the sketch you’ve done.
All the details of how to correctly use the embroidery machines (and the software) are on the toolpage. I’d strongly recommend going through this as the machine is not always intuitive and can jam your project if setup wrong.
I’m not an expert on this machine but happy to help where I can so do shout if you get stuck. I hope you’ll post these when they’re finished. 
Would be cool to see the finished product.