First, definitely take a look at, download and print the time and frequency lists from here:
http://www.eibi.de.vu/This is the most in-depth schedule for shortwave that I have found out there.
As far as credible sources, in my opinion, you will just have to spin the dial and checkout what is out there. There are lots of different countries broadcasting and each news source could potentially put their own spin on things. I have personally listened to news programs out of Russia, Cuba, Romania, China, Hong Kong (or something like that one night), US, etc. But, the news programs that I have listened to seem to be pretty decent about reporting the facts as they are with little to no interjected opinion or commentary. Even the Cuban and Chinese news programs that I have listened to were fine.
In a true SHTF, your best bet is to spin the dial and see who is even reporting!
Also, I am assuming you have a telescopic antenna on your receiver. For added reception, take a piece of 30-100+ foot speaker wire (can be any wire for that matter) and string it around a room. It can be at ceiling height (for best reception) or even tucked under your floor molding. Then just wrap a stripped end of the wire around the end of your receiver's antenna. This should greatly increase your SW reception.
HTH and have fun with it!