HollisOataheir:
Are you wanting to start the crew as beginning Edge of the Empire characters? Or with some amount of experience?
I have them built by default as starting characters in FFG. While the game I played had them go on quite a few adventures we never got around to talking about XP.
HollisOataheir:
Would you want to start them with their own ship already acquired?
As per RAW I had them start with a Wayfinder-class freighter. Them having a ship isn't required however the story would need to be altered. I'm fine doing a "prequel" type adventure where it is just a couple of characters and they slowly work their way to recruiting the rest of the crew.
OR they could have run into some serious bad luck and had their ship blown up or impounded or stolen. Doesn't matter to me.
HollisOataheir:
Are there any "must haves" from a story perspective (like the Hutts, Black Sun, etc)?
Nope, pretty flexible on adventure threads. So long as there is credits and a chance to snub their noses at authority.
HollisOataheir:
In what time period would you want to set these adventures (Old Republic, Rise of the Empire, Rebellion, Force Awakens, etc)?
As written it is set during the Rise of the Empire as per the default setting, however they would work out in any setting as desired. I would need to make minor tweaks here and there to fit Old Republic or Force Awakens but the beauty of the Outer Rim is that so much of it remains unchanged throughout the years.