I used to use Itoyas but lately have been moving them out into archival document storage boxes. You'll want boxes that are at least 10" x 11" (inside capacity) for standard sketches, and 9.5" x 12" for the newer "letterboxed" standard sketch size. It's a good idea to have at least one bigger one (I use 12" x 15") for oversized items. Look for those that are pH-buffered, not just "acid-free," as you want to maintain a protective inside environment for the sketches.
If the boxes are good ones, they should be light-tight, and you can store them on a convenient shelf in your room. You can also get "acid-free" clear boxes for scrapbooking material, which are OK for the short run, but keep these in a closet to avoid exposing the edges of the sketches to light.
I bag my cuts individually, with all the sketches together, but separating those on white paper from those on colored paper with a sheet of acid-free cardstock that is just a little bigger than the sketches. (You can buy this made to size, but I just wait until 12" x 12" cardstock goes on sale at the local Michael's or use one of their 40-50% off coupons.) The cardstock also provides a bit of protection to the corners and makes the set easier to handle and sort. This is especially so if you have only one or two sketches to a set, or if you are displaying a few separately from the rest. Those corners can get banged or even creased over very easily otherwise.
Lately, I've been including sheets of microchamber paper (buffered, with chemicals that attract and absorb gases that promote paper deterioration) inside each bag, usually on the side with the colored-paper sketches. I do this because I've understood that the colored paper has a higher acidic content than the white paper, and so is likely to deteriorate quicker and possibly damage sketches stored next to it. I can't verify this from experience, but it does seem that the sketches on thin yellow paper are more fragile than those on white paper. The manufacturer says that one sheet is enough to protect a comic-book-sized stack of sketches.
Bags and microchamber paper are both available for reasonable prices from
Bags Unlimited. The best boxes are available from
Light Impressions, but expect at least a 3-month delay, as I think these are not kept in stock but made in small batches once a critical mass of orders have been received. (I just got a shipping notice for the ones I ordered back in March.) But Bags Unlimited also sells boxes, as do other archival supply websites such as
Talas.
One hint: get every bit of celotape off any sketch that you plan to maintain. I've gotten sketches with tape than seemed stable at the time, put them away in Itoyas with others, then, some years later, come upon them while moving them to the boxes and found that the tape had begun to damage the paper under it. Get some solvent (I use eucalyptus oil, which I found recommended on a librarians' website) and get it off before the damage is too severe. Remember, it's the glue, not the tape, that causes the damage. It's then a good idea to bag any sketch that had had tape on it separately (with a sheet of microchamber paper) just in case some of the adhesive is still present and reacting with the paper.
Another: take an ultra-fine-point Sharpie (or generic equivalent) and label the outside of the bag: Series, Episode, Cut. Particularly for odd-shaped sketches or those you've gotten tape off of, so that you can easily file them with the rest of the sketches. Also if you display a sample sketch in a display book and store the rest somewhere else. That will help keep this part of your collection organized for you and your heirs and prevent having individual sketches get separated in a way that makes the cut difficult to reconstruct later.
Good luck and thanks for asking. One can only imagine the amount of original animation art that's gone on the market and simply allowed to deteriorate or get lost, and so I imagine future generations interested in anime will greatly appreciate those who take time to make sure that these materials are properly conserved.