I also came into the 3D world through animation years ago (Lightwave, Cinema4D). There is a difference in the mechanical design programs from the animation based. That has to do with animation programs being polygon based, and engineering design being parametric based, which is math based. The approaches to modeling are very different. Kind of like the difference between a pixel paint program like photoshop, and vector based program like Illustrator. However, both methods have their place.
I look at it this way-
organic designs- polygon based modeler
“engineering”- (basically anything that needs accurate, specific dimensions) parametric modeler.
Recommendations
Organic- Blender Has a very good sculpt feature in it. If you decide to learn that along with a parametric modeler, send me a message and I’ll give you a suggestion for beginner Blender tutorials.
Their is a BlenderSketch plugin to give you tools similar to parametric modelers, but it’s still in beginning stages ,so you do not have a full set of tools. Not ready yet for full scale design.
Free parametric modelers
For the ones with pay for versions in this section, if you want to step up to a paid for version, the modelers are subscription based. One time pay in the next section.
FreeCAD- always free. Powerful in many ways, but has some quirks in it you need to know. Also, a slew of tutorials, but from my experience, beginner tutorials across the board are mediocre at best. You will have some frustrations with learning it.
TinkerCAD- web based, free. Works well for really basic stuff, but beyond that, getting results can become very time consuming.
Sketchup Free- web based, better than TinkerCAD for more complex items. Have seen a couple of people that design for their print farms using it. It was designed primarily as a architectural program, but people use it for model and part design. No personal experience with it.
Shapr3D was already mentioned.
Onshape- free version is non commercial. It requires all of your models to be public and stored on their cloud at the free level. Not as steep of a learning curve as the other parametric modelers, but boy is their pay for program steep.
Fusion 360- most widely used. Has a number of limitations like all the others. Excellent program
SolidEdge Community Edition- Free, limits placed on functionality like the others. Another excellent program
DesignSpark Mechanical- limited features at free level. Appears to be a good program, but the tutorials available were mostly for older versions and the interface has changed so much, the old ones are worthless. I know because I went to try this one out. Just saw they’ve finally put out some new tutorials. Has the lowest costs of any of the subscription based modelers
Non free after trial, but not subscription based.
Plasticity- only free for the 30 day trial, and the cost for the first level (Indie) is not prohibitive, but be aware you only get one month to upgrade to the pro version after buying the Indie level w/o having to pay the full price. Probably the easiest to learn for someone with polygon based modeling experience as it was designed for that. Actual purchase, not a subscription. People coming from polygon modelers seem to love it in their reviews.
Alibre- has been garnering excellent reviews. Basic level is reasonable, but misses some key features like thread creation. One time payment, big jump in price from the beginner level to the pro level