Do not get amazon market. it eats up battery
First, I would stay away from using the Amazon market app. If there is an app with malware loaded onto your phone the Amazon Market doesn't have a way to recall/wipe the app from your phone like the Android Market.
I doubt the app is a battery hog unless you are allowing the app to send/receive data on its own like the blockbuster app will do until you change the settings on the app. I don't have the Amazon app. Typically noobies make the assertions you have made. Not harping on you, I'm just saying. I hope this helps.