As a test, I turned off everything except GPS on my smartphone, then turned the screen off. GPS and one GPS app stayed running. I got about 6 hours of GPS tracking with less than half battery usage. When my screen is turned on, that really sucks up the battery pretty fast. I do not have any SIM cards in my smartphone, I have no idea how much battery that saves me.

Regarding filling up your memory pretty fast, it is best if you plug a Micro SD card into the phone. Then configure your apps to be located on the external SD card instead of internal memory.