I have some experience with after effects, but only with very short sequences. Soon I'll start working on an animated education project of 1-2 minutes. Now before I do it all wrong, I thought I'd ask: Is there a specific way to tackle such a project to not lose control, or make it too heavy and slow? I Imagined if I had all these animations going on in there for several minutes, it would clog up pretty quick.
Break big projects down into smaller, more manageable chunks.
Stay organized as you go along. Do not ever, even once, put a file on your desktop. Build a folder structure for your project and stick to it -- the files go where they belong the first time, both on your hard disk and in your AEP. Name your comps. Name your layers. Think of a naming convention that is meaningful to you and use it as you work.
Don't even think of cheating -- "I'll just do this one thing quick and dirty, then I'll go back in and clean it up" -- no one ever goes back and cleans it up, and it will just bite you later on. Do it right the first time so you never have to do it again. When you see you've done something wrong, fix it on the spot. Otherwise, it will only get "wrong-er" the longer the project goes.
Familiarize yourself with the concept of technical debt [link], and think about how it applies to motion design: basically, choosing an easy solution instead of the "right" solution early in the process requires you to spend way more time dealing with it later on.