There are a few of those. Especially as first missions from a contact. (Tina & Maria for example) After that, it's fairly random unless you have too many arcs active already.
I've done the roulette wheel to get Maria's Siege mission for example.
And yea, abandoning is pretty forgiving. Even if you start a mission, come out, select a different mission from your list, choose abandon pregress, then call up the contact and abandon the mission, you can call the contact back and get a different one. It's how people get the Invader badge in 20 minutes by just popping into the Mayhem map, grab the explore badge, and exit. The mission holder is usually just hanging out at Lord S' location.