Onshape has not changed, it IS free but all your models are public if you are not paying, and non-commercial only.
123D Design is (was) pretty great at filling the niche in between TinkerCAD and Fusion 360.
It is also discontinued, so I am confused as to why it is being recommended. If you are lucky enough to have it already, hang on to it, but it won't be getting any updates, and anything in the cloud is gone.
If you follow along over at Autodesk Community, the changes coming are very transparent. Tinkercad is going to inherit some of the more "intermediate" features of 123D Design and not feel quite so amateurish (and why anyone would feel any sense of shame is beyond me, use whatever gets the model made!).
Fusion 360 is pretty awesome, very powerful, and a bit complicated, but there is a massive amount of free tutorials and learning resources for it. It is free for students, hobbyists/enthusiasts, and any business earning less than $100k per year. That is renewable annually. That covers pretty much everyone in here.
Personally, I use both 123D still (offline mode) if I need something easy to model and to get it done quickly, and Fusion 360 if I have more time and it is more complicated. I can certainly say I still have a lot to learn there too.
For more organic style modeling, there is Meshmixer, which a lot of people love (not me), and Blender is another excellent free app with a huge following, lots of support and training available. ZBrush is amazing and expensive. Both are great tools. I am by no means a Blender expert, but that is the app I am currently studying. It has features that lead into 3D animation as well, but I stop at the modeling part, so I don't worry about the rigging and timelining and all those features.
At the end of the day really, the best modeling app is the one that you can make things with and feel comfortable. Once you can do that with one app, keep doing it AND pick another one that makes you uncomfortable and start learning again. This is 3D Printing, if you stop learning you get left behind fast.