FreeCAD should be able to make what you're looking for, but is a bit clunky. If you're new to 3d design I would recommend Onshape as a near professional level CAD tool that runs in your browser. You can use it for free, but a free account does not let you keep your documents private. I just use it for odds and ends so I have no problem with my documents being public. Onshape also has a lot of tutorials that cover a lot of the basics of 3d modeling. Another option would be Fusion 360, since it also has a free subscription tier, as well as a lot of tutorials. I'd say that Onshape is easier for a person who's new to 3d CAD to learn on, but your mileage may vary. Another option that some of the people around here use is OpenSCAD, but I have no experience with it and would have to defer to other community members to answer any questions you have about it.

As to your gear question, I'm not sure there is a simple answer. I'm unfamiliar with the FCgear module, but I imagine a good spur gear script/module/plugin/whatever will probably get you the most details for a real gear the quickest. If you're fine with something close enough but not perfect, you can try modeling it yourself. Below is a starting point for you that I got going in Onshape. I'm not 100% certain that I interpreted your description correctly, but it should give you something to work from. Let me know if I can answer any other questions.

https://cad.onshape.com/documents/77...6b596150a45d50