Cardboard is bad bad bad bad bad.
Did I mention it’s bad?
Anything that could be purchased in a retail arts & crafts outlet, or art supply store, not specifically labeled acid and lignin (sp) free should be avoided at all costs.
Ideally, get yourself a sheet of 4 or 8-ply cotton rag mat, cut into whatever sizes you want to mount them on. Use an acid-free reversible adhesive, or if you purchase matting for the front part you can also use something like the archival scrapbooking photo corners to attach it to the backing.
Don’t mash glass on it, it will stick eventually. Either mat the artwork so the glass doesn’t touch, or have acrylic cut for it.
If you really want them framed to last, though, unless you’re planning on doing many of them, you’re probably better off just getting the one or two you really want preserved, framed professionally. To do it right will cost money regardless of the route. Otherwise you can always just frame them with stuff off the shelf, but if you want them to be in top shape 50 years from now I wouldn’t recommend it.
And cardboard is evil.