You are right, that the sentence should have the word "the" in front of the word "before". The correct sentence should look like this:
"It has some of the finest universities and probably best overall school system in the country."
The word "overall" means all things considered. For example, I could say "the corvette is faster, but the porsche is a better car overall" to mean that if you look at all of the features together, the porsche is better.