+1
After you do this and it dries, put some vaseline on the terminals and it will keep the corrosion from coming back for a long time.
As for terminals ... you could get some like these:
They are gold plated and work excellent. They are like 25 bucks for both of em' and super easy to put on. You just cut off the old pieces of junk right where the wire connects and then strip it down just a little, then slide the wire into the new connectors and two screws tighten down to hold it on. And on the positive terminal, there are hex screws that hold the wires in (even easier) and plus it has like 4 slots in case you have speakers or other accessories that need to be connected to the positive terminal.
Just a thought ... I got them at like Autozone I think.