Shows the battery saver active message

My car listed above SS model will show the battery saver active message and after a while will almost completely shut off. All lights and gauges will turn off and the car will stay driving until I slow down to turn. Then it will stutter and act like it wants to go but won't. If I floor the gas pedal it'll stutter for a minute but then it'll take off and all power comes back like nothing happened. I have a new alternator I can put in but should I try a new battery first? If so, any cheaper alternatives for a new battery? All I find is 199+ for a new battery online and part stores.