1. Integrity issues:
- on Windows launch command line with admin rights
- CHKDSK C: /F (and if game is not on your C: drive check these logical disks too)
- SFC /SCANNOW (this will attempt to restore Windows OS integrity if damages)
- from game launcher select REPAIR (this will fix problems if the game files are corrupt or modified)
- rename file ShaderCache.cooked in your /documents/Elder Scrolls Online/live folder to ShaderCache.bak (this will make the game to re-create it, as it might be damaged too)
- clear NVidia or AMD shaders cache (google how to)

2. Hardware issues.
on Windows launch Control Panel -> All Control Panel Items -> Security and Maintenance -> Reliability Monitor
if there are Errors - google how to fix these

3. Overheating issues
use HWmonitor software (or similar) to check your CPU, GPU, SSD temperatures, anything above 75C should alert you.

4. Error 307 Booted from server
update your addons (some may use excessive information exchange with server, which causes your 15 minutes "timeout" for "too many messages", though this is not you who produce them messages, but your addons do)
minimize the number of addons you use

and, just in case: backup your SavedVariables. this is irrelevant to your issues, but, trust me, re-tuning dozens of addons after abrupt game crashes is rather burdensome

I was trying to turn some items I got in the Crowncrate into gems. And then the i got disconnected and upon log in I get a 307... Did I do something wrong?