A cheap option is to get a child's sports mouthguard. You can find them for a few bucks at any Wal-Mart or Target or K-mart. Not real expensive and you can mold to fit and since the mouth is changing all the time then you won't be spending a ton of money when you need to switch.
Teeth grinding can lead to muscle cramps in the jaw which can deter eating and talking (I had that problem) and it can also lead to migranes becuase of chemicals released when the grinding occurs. Keep an eye on it to make sure these complications aren't showing up and if they are see if they are related to the grinding.
Best of luck with it!