Thank you for your kind message. If you come from a graphic design background (specially if you thoroughly studied its theory and practice at school or by yourself), you have the most important ground for starting to work in motion graphics. You only need to focus on the animation aspects of it. I came the other way around: from animation to design, so I had to struggle more with learning design principles.
I would say there are two main ways of working: by necessity, when you get a paid commission and you do a lot of research to achieve the requested goals, or disciplining yourself into doing tutorials regularly… Or ideally both. As I said, I cannot provide much advice on 3D.
As far as After Effects goes, what it does is arranging 2D planes in a 3D space. It’s like when people did visual effects in films by arranging several painted plates in space and then filming them from a certain point, to make it look like a real life landscape (think Star Wars paintings in the 1st trilogy) - this is the kind of “3D” I have more experience at and it’s affectionately called 2.5D. Again look for tutorials for different types of tasks with AE and you’ll find even particle SFX that can be worked with AE using plugins like Red Giant, Boris FX, Element 3D, etc… Then you can even find lots of scripts for AE, which provide instant FX that are most useful and configurable.
Rhythm - it’s good to have a good notion of rhythm when animating.
Timing Events - remember human attention tends to focus on one thing at a time. Don’t get a lot of stuff happening at the same time. Don’t have everything animated at once. Let one thing move and keep the rest static. Then change.
Readability - this is something we had to pay tons of attention when PAL or NTSC 4:3 SD interlaced Television was the norm and most people watched TV on CRT type TV sets. You had to be very careful. We had to avoid pure whites or pure reds as they would get too blown and flicker a lot. Nowadays we don’t have those issues but we still need to be careful with what colors we mix and using parsimoniously outlines or drop shadows to improve readability.
Action-Reaction - this is a law that most people often forget when having several graphic elements interacting with each other. Gravity, physics, objects affecting other objects… Making everything interact with each other like in a dance. Things have to have an intrinsic harmony based on cause effect, when interacting in a scene.
Anyway… We could go on forever but, these are some “not so usual and common” recommendations I can remember from the top of my head. Stuff not so often mentioned out there.
Hope this helps.