dh and i are admitted book hoarders. when we moved the bulk of our boxes were books. we have what many would consider a very large bedroom that has wall to wall (all four walls and the closet) with ceiling to floor bookcases.
that said-as far as kid's books go. as a former teacher who saved hundreds and hundreds of books for that 'someday' i'de suggest that unless your kids are reading/will read or you plan on absolutly teaching the age range the books you are keeping are appropriate for-consider donation or using them for trade in credit at a used bookstore.
back when i became a teacher, in the state i lived in, we received multiple subject credentials for k-12 so we could end up teaching (in a traditional public school classrom) any grade from k-6th (though there were the actual "one room classrooms" in existence where teachers did and still do teach k-12
). these days it seems like it's more specialized with the lower grades (k, 1-3) and the upper (3 or 4-6th). that said, depending on what kind of credential you are looking at, and what your state's norm is-holding on to hundreds and hundreds of books is'nt as necessary as it once was.
when we did our most recent move i went through dozens and dozens of boxes of books preparing to shelve them as i'de done with previous moves. the realization hit me-many of these books had not been opened nor could be expected to be opened in years and years. i thought to the appeals our local libraries and schools had done for books and considered what i needed/wanted to keep. i opted to keep those that held sentimental value to myself/dh/my kids, and what i truly thought would be beneficial to the kids in the future (books they had'nt yet hit the age to read). i cleared allot out to very welcoming recipients.
as for storage in general-i put paperback (berenstein bears and such) on their sides in bookcases with hardbacks on their ends (protects the spines), misc. softbound in cloth baskets or magazine type holders with labels by subject matter (nature, science, historical....just as the library does). i have shelves at the top of my bookcases that have books my kids have long outgrown but i wish to retain (primarily little goldens dating back to the 50's and 60's, some disneys and sesame streets). i keep the ones they are apt to read at their eye level-and routinely insert books that they may become interested in or i want to encourage them to consider.
if storage is a major issue try to connect with someone who sells avon. the reps get these awsome lidded boxes that are ideal to store items in. i would'nt reccommend putting books in them to schlep into the garage or any other non temp controlled place, but they work realy well for storage in closets.
of course I'm not sure what else would work
I have many children's books as well. 
- horizontally so they made book holders so I can stand all the books faceout. It worked pretty good - though naturally I had too many books for just one wall like that and again it looked CHEAP!
