Welcome to the wonderful world of graphic design.
The answer depends on your intentions - where do you intend to go with your design. If you looking to become a graphic design, taking in branding, print design, and maybe a bit of animation then it's pretty much Adobe creative suite.
Something like that graphic can be made using illustrator and after effects. You'd draw you're flat logo in illustrator - bring it into after effects - extrude it (give it depth) add a material and spin it. It's fairly simple, and there are a million youtube tutorials showing you how to do it.
If you want to get into motion graphics exclusively, then you might want to learn a 3D/animation program. There are loads to choose from. By far the easiest (in my opinion) is Cinema 4D. It is relatively easy to pick up, and integrates well with after effects. The tutorials are good, and there are plenty out there. you can get very advanced with it (for instance, the film Cloudy With a Chance of Meatballs was made with it). The downside is that it's VERY expensive for a beginner. Blender is a free alternative, which is very good but a bit harder to use in my opinion. I'd say the best way to get into 3D is to download the Cinema4d trial - hammer tutorials for your 40 days. You won't be able to render anything without a watermark, but you will learn the principles of 3D animation, which will help you when going to something more complex.
Hope that's some help.