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Replace the Battery

I think you should get an Apple Battery. Also, unlike Android cell phones, you dont just pop in a battery. There are videos about how to do this but if you arent careful, you could brick the phone. Just take it to an Apple store or an authorized repair shop. The latter may be cheaper. They will know what battery works well with your phone.
Well I don't get that many calls now so when I get the iPhone Activate with Straight Talk or TracFone I can live with the battery that in my iPhone. I can leave it on the charger when home and 13 hours should be good enough when I am not home.