I've done a few schools before, and my advice is as follows:
Break it down into bitesize chunks for quoting purposes (as has been said).
Get the janitor to show you around. Not a teacher, nor an administrator or anyone else. A good way to do this is to tell them you'll need to know where the water access points are. The only person who will know this is the janitor, so (in my experience) he will be asked to show you around.
The janitor is the one who knows what needs doing and what doesn't. He is also the person who will be your champion to the finance bods when they are ready to keel over at your price. Get him on your side, and you've pretty much got the job. Be polite to him, NEVER swear in his company (remember he is around children all day, so has trained himself to curb swearing. He will notice if you swear and it will play against you.)
There's no need to go in cheap, that is totally self-defeating. A high price will be accepted if it is framed correctly, and championed by the janitor.
I would be against making demands like removing tape etc from the insides, as they will be very unlikely to be able to comply with it. (Who will do that? The teachers? Ha no. The janitor himself? too busy!). Instead, give them a choice. Either you can miss those windows, or for an additional 5% you can remove the tape yourself. (I would never remove posters or artwork from the windows, that's a class's work and they probably want it there).
Some schools will ask if you have a CRB check (or whatever it's called these days). If you do, great. If not, say not at present, but you have no objection to having one done if the cost of doing so is met by the school. This tells them that you've nothing to hide and most will simply drop it there. If they're willing to pay for it, all well and good. (If you have criminal convictions that will show up on a CRB check, don't even bother replying to a school asking for a quote).
Schools can be very profitable, easy work if you get them right.
Good luck!