Well, for the cost (free) Blender is a pretty capable all round 3D program. It actually does far more than most others out there that you have t pay for. It can be used as a Video editor as well as 3D modelling and animation and even at present has it's own game engine. It's the best bet on a budget. Max could be better in some ways, especially if you have a lot of cash to buy plugins to streamline production. It's still the main software used in the industry, mainly because it's used by most companies and hence taught in college etc.
I'm no expert in either though but know they are more than capable in itself to do great animations. The problem in the past (for me anyway) was getting an animated model from Blender to GG. The formats supported by GG tended to be non animation ones like obj. I had no issues with simple rotations as mentioned above with .x, but any bone based stuff I tried always sat like a statue (in GG).
There may be other options out there better suited possibly, but Blender covers modelling and animation pretty well. Sketch-up as far as I know is only for buildings and such and therefore does not support animations. But again I am only going from using it many years ago, things get updated occasionally
As mentioned above, for youngsters 2D may be okay, they aren't likely to snub it because it isn't shiny and 3D. If we get to that point the world is doomed!
SPECS: Ryzen 1700 CPU. Nvidia 970GTX. 16 Gig Memory. Win 10.