J.D.
I keep a binder for each child and use those plastic page protector sheets. All report cards, awards (school and non school), some artwork, etc. go in the binder. I'll keep writing samples (especially if it's an original writing vs copy from text kinda thing). At the end of this last school year, I went through all the notebooks and ripped out the pages I wanted to keep then pitched the rest.
I wouldn't keep textbooks unless you are truly the kind of parent that would use them over the summer to review. If you're not, then give them away - freecycle them or offer free on craigslist.
Once my guys get a bit older (they're heading into 3rd grade), I'll have them join me in the sorting process. For now, I know I want to keep somethings, but I only keep a very limited amount since it could accumulate to a bookshelf full of binders!!
I chose the binder/sheet protector method since most reports/awards are of the 8 1/2 x 11 size and even the smaller things won't get lost in there. These books can be taken down anytime and flipped through without fear of ripping a page or papers everywhere if you used a box.
Good luck,,,,,don't stress, enjoy the trip down memory lane!
J.