What is After Effects?
After Effects is a compositing program, not an "editing program". The most basic example of what "compositing" means is using a green screen when recording, keying it out and replacing the background. In a normal NLE (non-linear editing) program, you're cutting and arranging scenes to form videos. In After Effects, you're combining footage, graphics and effects to form scenes. People also use AE for motion design (animated graphic design), animation in general, special effects and yes, people also use it to make their entire AMV from start to finish.
The point is, AE is made for compositing not scene selection, cutting and arrangement. So while it's not impossible to do all of those things, it's important that you do not expect it to be as easy as in programs made for those things. AE expects you to already have a video at least planned out. It's easiest to use Premiere Pro for that, since it can send your project (with all of the edits intact!) to After Effects with a single click. You can of course use anything that exports video but if you use a rendered video you lose access to your edits and can't change them (without rendering and importing again).
I personally hate Premiere Pro so I cannot make a reasonable guide for it. Thankfully Adobe has commissioned the people who already make tutorials to make official ones. If you want to learn Premiere Pro (which I recommend you use in conjunction with After Effects), check out this 2h tutorial. You don't have to watch all of it in one go.
Should you learn After Effects?
So what is After Effects good for if you shouldn't use it for scene selection? Scene selection is everything! Well, you most likely do not need to use After Effects. But if you want to do any kind of "technical" editing you want After Effects (or DaVinci Resolve or Blender or Final Cut or Vegas POST, I guess). Anyway here are some examples of what you can do with After Effects:
Compositing, motion graphics
MMV
Effects spam :3
If you want to do anything like that or you're just curious, you should learn After Effects. If you don't care about flashy effects, hate masking and the idea of compositing your own scenes instead of just using what the animators gave you makes you sick then no you shouldn't learn After Effects. I recommend checking out Vegas Pro.
Should you learn After Effects using amv.tools?
The After Effects guides on amv.tools are meant for intermediary to advanced level editors. If you are new to editing, hate reading or feel you need very methodical and specific instructions, amv.tools guides are not for you. This is not a bad thing. Amv.tools guides are meant to be a reference for established AMV editors, showing how to do things you already (at least sort of) know but with a new program that you're not accustomed to. This is not to say you can't learn After Effects as a beginner using amv.tools, just that it might be harder to do than with a guide specifically made for beginners.
If you're confident in your editing abilities or you prefer text guides, you can get started with learning After Effects from the sidebar or the arrow on the right to take you to the next guide, basics.
And if I scared you away from amv.tools' text guides, here are some video tutorials: