There are so many variables with this I almost don't know where to start. There are many, many kinds of shower heads. In addition, some heat with gas and some electric. However, I do know this: a low-flow shower head will save you money.
If you want to be super duper frugal and save the most you can, you could purchase a navy shower head. You can turn the flow of water off with these so you can suds up with no water running. Personally, I'm a little more spoiled than that, but somebody might love this idea!