For the system usability keep the Lite now. And keep checking updates regularly for any fix.
And for the troubleshooting part maybe logs will give some clue where is the issue. First switch to gdm3, then login your system. When you reach the Something went wrong screen, launch terminal or switch to TTY, run the following and share the output links:
Thank you for sharing the logs, however (I should have mentioned it earlier) I am not that experienced to understand such logs properly. I hope some experienced mind will give it a look for analysis.
However I have one doubt, unrelated, how the debian jessie repository present in your system?
packagekitd[2175]: Index of /debian jessie Release is not (yet) available (404 Not Found [IP: 2a04:4e42:8d::644 80])