Oh boy, here we go…
There are several packages you might consider. Debates over 3D applications can get as heated and petty as Mac vs. PC or Bing vs. Google arguments. I’ll try to be objective in the comments below and clearly state what is opinion and what is fact.
There are two heavyweights:
Maya (Autodesk) - This is my favorite 3D application, and the one I personally use. It has full support for modeling, texturing, rigging, animating, and rendering. It’s the most common application for 3D animation and has tutorials across the webernet for all of itsfunctions. You can download a free educational version from the Autodesk website.
3DS Max (Autodesk) - This program is very similar to Maya. many say that it is somewhat better for modeling but slightly less useful for any other function. I’ve used it quite a bit yet never found a way in which it’s better than Maya. But that’s just my opinion. Max seems to be the favorite program among the VEX community. You can download a free educational version from the Autodesk website.
Three other programs on the next tier:
Blender - A free, open-source 3D package. I’ve never used it, but from what I understand, it’s not as functional as Maya or Max but it has a shallower learning curve. Though it probably has less tutorials because it’s not as popular.
Cinema 4D (Maxon) - I haven’t used this program either. It has a smaller community than Maya or Max but I’ve seen people make amazing stuff with it. I don’t know that there’s a way to get it for free.
LightWave (NewTek) - I’d give this the same description as Cinema 4D. Oh, and it’s supposed to be really good for making spaceships. I don’t know why.
Those are the big 5. But there are a bunch of other programs as well: Softimage, Houdini, Rhino, Zbrush, Mudbox, Sketchup, and Modo to name a few (some of these are not standalone and/or are less practical for use in a robotics animation).
Then there’s compositing software for editing and postporduction. After Effects is what I use, and it seems to be the most popular for special effects, motion graphics, and 3D compositing. But a lot of people will use Nuke for 3D work because that’s what it’s specifically designed for.
Oh, and rendering applications! Mental Ray, V-Ray, RenderMan, FinalRender, Shaderlight, Maxwell Render, Brazil, Fry Render, Octane Render, Arion Render, POV-Ray, and the rest. Don’t worry about these too much.
This is by no means a comprehensive list. So yeah, good luck picking what you want to use. Skal!