I've built books before, built about 5 back in college. 8-)
For endpaper, I've used something that is sturdy (but not rigid) with a pattern. Something that turns easily. Don't want it to rip easily. Something that won't ripple if pasted to the inside cover. Perhaps
I'd avoid construction paper, as it comes apart too easily when wet and ripples when glued.
Since you want something plain, I'd suggest checking scrapbooking stores or paper wholesalers if you can find one. Here are some photos of one of my books:
cover
inside cover