Upgrading won't change configuration files which you have edited. If you've edited a file and the default file has changed, you'll be given the option to keep what you are now using or use the new file. You'll also have a chance to examine the differences. That said, there shouldn't be to many changes from 13.10 to 14.04.

Taking a snapshot of the image before upgrading is something you definitely should do. I'd also encourage you to make off-site backups of critical files on a regular basis. Especially your database:

https://digitalocean.com/community/articles/how-to-backup-mysql-databases-on-an-ubuntu-vps