I'm such a HP nerd, I've thought about a lot of this and talked about it on other forums.
www.hp-lexicon.org/essays/essay-secrets-of-the-classlist.html
This essay has a list of all the students in Harry's year, breifly shown in a TV documentary years ago. Apparently there are 40 students in his year, probably evenly divided between the 4 houses. Basically, what this shows is that Harry is pretty oblivious to his class mates, as he doesn't even know the names of everyone in his year at school (or ever notice them, despite sharing classes with them). It's entirely possible there are even two other gryffindor girls that he never once speaks to in seven years of school!
With the teachers, basically none of it makes sense. Those teaching core subjects have an awful teaching schedule- McGonagall, for example, seems to have about 22 classes- unless students only have one transfiguration lesson a week (which seems unlikely), when does she teach them all- never mind doing her pastoral duties as head of house. Snape's schedule is a bit kinder, assuming all his lessons are joint between two houses, he has only 12 classes, but that still only really leaves room for an absolute maximum of two potions lessons a week.
The teachers who teach 3rd year electives probably have a smaller teaching schedule, teaching between 5-10 classes each, so it would really make more sense for them to do most of the pastoral/administrative duties, but poor McGonagall seems to have to do everything from sending out letters before the start of term (can't Hogwarts affor a secretary?) to pastoral care for at least 70 children, and she's deputy head.
The numbers in the school (in Harry's year at least) don't translate to the size of wizarding population that's supposed to exist. Some students can be home schooled or educated abroad, but it seems pretty heavily implied Hogwarts is the only wizarding school in the UK, and possibly the whole British Isles.
I do think Hogwarts is a state school, though, given the level at which the ministry can intervene in book 5. They just take a laissez faire approach, most of the time. However, students seem expected to pay for some really expensive kit, which probably explains why most of the Weasley's stuff is second hand.