We have a site very similar to what you described in town, although the school was torn down a few decades ago. In addition to the massive amounts of trash that accumulated while it was an unmaintained vacant lot, there's also an astonishing amount of building materials in the ground - door knobs, sprinkler heads, LOTS of chunks of dressed stone, pipes and rebar, etc. It's almost as if they simply pushed the building over and covered it up with a few inches of dirt.
There's another old school site in the same general area of town and it's the opposite - no building materials at all, and not a lot of modern trash either. Unfortunately they probably filled the heck out of it, so all that trash (and the goodies) are probably still there...under several feet of dirt, anyway.
There's a third one only a few blocks from me that's essentially clean; one can walk for long periods of time in all metal and not hear a chirp. The one and only time that I went there, I did a compete circuit of the sidelines and found one bottlecap and one dime. I suspect that someone is hammering the crap out of this place, as there's absolutely no reason for so little trash to be there. No sign of the school or its inhabitants, obviously.
I guess what I'm trying to say is that you won't know what is or isn't in that field until you've put a coil over it in its entirety. There's no other way to be sure.