What purpose does the overall order of reaction serve? Once I've calculated it, what information can it provide me with?
It shows you how likely a reaction is to occur, and the rate at which it occurs.
It is more important when it comes to actual practice. There's not much you're able to do with it in the school setting other than holding on to it for higher level classes.
In industrial processes, it's quite an important concept. Use of certain reagents can make for a range of different reaction pathways, so it pays to use a reagent that produces the maximum yield of desired product at the lowest cost possible. Efficiency.
In biochemistry/pharmacology/medicine it helps you to understand enzyme functions, and the pharmacokinetic profiles of certain medications i.e. the half-life of drugs, peak plasma concentrations, toxicity, drug-interactions etc.
If you can understand it now, it may be really helpful to you in the future depending on what it is you're thinking of doing.