Mike,
I would try to learn as much as you can about plastics. Most consumer products these days are made from plastics so your model may be plastic or it may just simulate plastic. Find out if they have REN foam. That is a great material to work with. It cuts and sands like wood and can be painted.
Common plastic materials that are machined are Delrin and polycarbonate.
I would look for way to join parts together since you may find that to create a prototype you may scrounge parts off an existing item to make your prototype. Or, you may need to make smaller parts an join them together to make the model.
You probably want to learn about finishing techniques. If you make a model, you probably want to paint it and take some photographs.
Learning how to use a vertical mill and lathe are great skills. You can buy some surprising affordable tools for your home shop. Look an Amazon for reviews and Harbor Freight Tools for some low cost (sometimes cheap) machines. If you don't plan to outfit your shop, ask about techniques you can use at home with simple tools. A drill press with a drum sander may do what you need. Dremel tools are another low cost option.
SLA or 3-D printing is a fast (somewhat expensive) way to get the shapes you want so you can paint your model.
www.printapart.com does a great job and you can get fast quotes.
Don't disclose any inventions that you have not protected. It may be best to learn on something more mundane.