Congrats!
My sister's a teacher, over the years I got to hear a lot about her board, both good and bad, not jsut bitching but she would run a lot of things past me for a sanity check because of my experience in public-sector labor law, and the same with a friend here who is a senior person with one foot in the administration and one foot in the teaching end of a local district. Sometimes their boards were good, sometimes not, and sometimes nepotism, borderline corruption, or just plain non-merit-based decision making reared their ugly heads. Some take-aways I have from their experiences:
Saving money is good, but the function of the school district is to optimize the quality of education vs. reasonable cost, not to provide the best education possible at any price or to provide the minimum legally-required education at the lowest possible price.
If you hire any senior administration people, track records do count, but a lot of them sound a whole lot better than reality will prove. You're asking for trouble if you don't thoroughly check up on what people tell you they've done, or don't understand what something actually means even though it sounds good, because the education field is full of BS awards and recognition that don't mean anything, really, or can even be more-or-less bought.
Unlike a small business, your relationship to the employees and professionals in the school isn't a two-player game, it's three (The administration has its own interests distinct from the board's) or even four if there is a strong union. If you go with the military approach of backing your suordinate (The superintendant and/or principals) no matter how bad s/he's stepping on it, you're looking at the losing end of a lawsuit sooner or later.
All the unemployed art history majors in the OWS encampments are a malfunction of our collegiate education system, not the K-12 one. K-12 education is supposed to provide a general education so kids can have a chance to figure out where their strengths are and pursue them, while picking up the skills they need to get started and some broad cultural context as more-or-less literate Americans to include things like art, music, foreign languages other than Spanish, and other stuff that gets nickel-and-dimed out when the sole focus goes to meeting minimum state standards as cheaply as possible. If it was just about teaching them a skill they could immediately employ upon graduation, we'd only teach them how to wait tables and drive trucks.