When your Mac is asleep, it's mostly off. There's just enough electricity being used to keep the contents of the memory (RAM) intact. If it wasn't for that, it would just be off.
Go to System Preferences/Energy Saver and set 'Put your computer to sleep' to Never. Set 'Put the display to sleep' to whatever suits you.
If you have external hard drives, you can check the box to sleep those devices. They will cause a brief delay if data from them is requested while they are sleeping, but it shouldn't cause any problems.