Formatted phone, including system I was going around TWRP recovery and tried a few things and then I accidently wiped my entire android system. Now I am left with the custom recovery and a phone that gets stuck at the bootloader warning. I can't seem to flash any stock rom to the phone. I am using a Moto G3.
You need to either restore a TWRP backup, flash a custom ROM and Gapps, or use fastboot to flash a current factory image.

Moto factory firmware images are unzipped and flashed with fastboot, they cannot be flashed with TWRP. The best source for instructions and firmware images is XDA, do not use the ones on Moto's website, they are older images and will likely fail with a "Preflash Validation Error" due to being older than what is already installed in the device.

XDA - Moto G 2015 - Factory Firmware Images
XDA - Moto G 2015 - How to flash factory firmware images with fastboot

Be sure you have the correct image and version for your device. Flashing an incorrect image can cause the device to be completely non-functional (bricked), and flashing an incorrect or old version will fail. 

Be aware that Moto has recently released several security updates and patches for this device, especially outside North America, and some of the firmware images are not available yet.

Flashing a custom ROM and Gapps is nothing more than copying the ZIP and gapps to your device, flash them with TWRP, and reboot. ROMs can be found at number of sources.

Of course, the best way would be to restore a TWRP backup of the system partition, if you have one. If not, one of the above methods is necessary.