I started with making 3d models of objects and weapons for games 15 years ago. Usually based of existing pictures or blueprints. Copy existing stuff is easy, even without measurements because good pictures with good camera can still be used for scaling stuff. I used to have about 100GB picture archive of all sort of stuff to be replicated into 3d models for game us.
Getting to know the tooling before you make something new really is the way to go. I currently use Freecad and Openscad. Freecad really has a way to work, sometimes going at something from a certain direction really helps you curb the complexity and pitfalls you can get yourself into.
I can suggest most of the videos made by https://www.youtube.com/user/cad1919/videos on youtube. Usually videos without audio just doing the modeling. Often I am surprised at his route to completion, usually fairly efficient and direct. For the item you want to make I would suggest following his example.
You should draw it out on paper in maybe 2 or 3 perspectives and do all the hard calculation and then just replicate it in 3d.
Freecad is really as user friendly as it gets for actual good small tolerance Free CAD. There are however some usability and or nagging issues. Like how you break your model and can't continue the route you had because the chamfer or join brakes your mesh :).
On a side note are you sure your idea is novel and new, I assume someone has made it before and you can copy ;) a few months ago there was a N mechanical mechanisms link on hackernews, it might be in there :).
Edit: don't look at the videos you find on youtube and just copy the thing their making. Make your own stuff just steal their workflow.
Also do everything using coordinates and measurements not drag and drop. Might help you visualise it better.