What asiababy said, if possible.
No, there aren’t proprietary sizes, but make sure your paper fits (use standard sized paper, not custom sizes); otherwise it gets really faffy. Also, if you have to cut the laminate, it’s not very safe for children, or the teacher, because of sharp edges.
Can’t remember brand names, but don’t go for the cheapest plastic cased ones if you have a lot to do; they don’t always heat up to a high enough temperature so you get bubbles in the finished product. Kids love messing with stuff like that so they won’t last as long.