GSM connections can have peaks up to 2A, so should be a super cap near GSM supply maybe 0,8F-1F 5V .
500mA is maximum supplyied to USB dongle 3G 3.5G 4G dongles, so there is a limit to 500mAh, Wifi can go up to 200mA durring TX and 40mA during receiving, but low power mode can go much less.
Batt capacity similar to smartphone 2500mAh. Use LifePo4 tech to have +2000cycles charge/ dischrage vs 600cycles lipo.
Check this cell.
This one is LiFePO4 high energy density 5Ah 100g
If @1A discharge (0,2C) life go up to 4000cycles charge/discharge or more if less current used. LiFePo4 can reach 6k-8k cycles with low current.
Make sure you use also good DC/DC for your system. Most DC DC converters are not efficient and keeps discharging battery even with no load. LTC1700 is a perfect converter max 4A. Please contact for any modules wifi, bluethoot Low energy, batteries or other components.
You can also cover back of phone with mini solar cell for enegy harvesting to charge battery, and use vibration energy harvesting.
Before develop any system think well about power suppy. Supply is supply, must be stable, efficient and very low conspuption by it self.