Aftereffects is an extremely advanced program, and you should really only spend the money if you want to spend a lot of time on post production and learning how to use the program. Also, Aftereffects is for videos, and really, stop motion is more single pictures than it is video clips (depending on capture program/camera). I know Photoshop can be purchased at a lesser price, and as a photographer I already had it, and can do similar effects as Aftereffects, because the animation starts out as single frames.  I tend to avoid post production anyway, so I'm not planning on buying any new programs.  If you do want Aftereffects and Premier, purchasing them both at the student price would probably be the same as buying the whole Production Pack, so you might as well get all the other stuff, because they can be very useful, especially Photoshop.

Opinion Stated.

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After Effects Cs6 is awesome! The biggest thing I think think alot of us like is the masking options. Yup. Now it's a lot easier to mask regular stuff like jumping up and down. To the update thingy, I don't think you can upgrade with the student teacher edition. Correct me if I'm wrong. It also speeds up post production a lot, but most stuff can be done in gimp/photoshop. Now if you're doing live action action also, then this is worth it. Now if you're only doing stopmotion, and you have a lot of time on your hands, this may or may not be worth it. For sure, try the free trial first though. As for the gear, LEGO can be fairly easy to save up for if you get some smaller sets, but what gear do you think could make your stopmotions even better?

EDIT: Are you sure you can't get the disk edition?

You should buy FXhome HitFilm.

I'd spend money on After Effects but you really need a nice computer. I've given upon AE after using a trial version with only 4 gigs of ram and an AMD equivalent to an intel quad core.

   

#1. Is it even worth it? ($440 is a LOT of money.)
#2. Would this be the best use of my money? Or would more Lego and/or better equipment be a smarter choice? (If the latter, please specify.)
#3. How long would I be able to use this without paying for an upgrade or newer version?
#4. I'm really just wanting After Effects and Premiere Pro, is there a way to get those cheaper and avoid buying all this other stuff that I'll never use? (Also, just how much of this will I really need?)
#5. This is the disk version that, as a homeschooler, I can't qualify for. But I can get the download version. Is there a way to get the disks anyway? Or would I have to go the download version?

A fellow homeschooler? Awesome!

Anyway, back to subject; Is after effects worth it? Yes. Although I've never used it my self, I've seen cool things done with it, and you're getting it for a bargain(I usually see it for around $1000).
A cheaper alternative? FXHome's Hitfilm looks pretty neat. And if my two cents isn't too late to pitch in, I would check that out.