FYI i am sooooooooooo hammered right now so i apologise if this makes no sense and i will do my best to fix any typos too...but im def not over generalising...the OP is saying an 18ft x 24ft stage...this would give some serious hot spots (from my experience) if you are looking to light up the stage from 20-30ft away (from the front) thats a different scenario and even then maybe. but if you are lighting this from the very front of the stage (in which is my assumption from my experience of most school environments) then you NEED a 30 something degree wash otherwise the hotspots will occur.
from my experience lighting has to do with (for front washing more specifically) to get as even light as possible...anyone to disagree with this??
I've seen 18'x26' stages with a trim of 40'...at 40' a 10 degree beam would be 7' wide by the time it hit the stage- more than ample as a wash as it covers roughly 1/3 of the stage
at a trim height of 10', the same fixture will only have a beam that's 1.7' wide, meaning it will take more fixtures for the same coverage, although you will have a much greater intensity at a closer distance than at a farther distance due to inverse square law (the same physics principle applies to audio...go figure).
it's about using the right tool for what you're looking for....if you're doing a single venue or venues that have a fixed trim height, you're generally ok buying a fixture that has a fixed beam angle as you can get close. if you're going into venues that have trim heights/throw distances all over the place, ultimately you want something that will zoom.
our go to LED par is the Microh LED Zoom Tri, which goes from 10-60 degrees and is comparable to a S4 par. I believe they retail in the $800 or so range, but I'm not certain on that.