So, today I made a new character, did the tutorial, now that character is Rank 13.
There was no way to just launch solo missions, and my contacts would not call me to do missions, even after I was at the right rank prerequisite. I ended up using the phone to do Quick Contact Jobs. Thankfully, nobody left these missions and they usually involved huge amounts of RP and Cash.
Eventually I got a Gerald mission, and since then missions now appear in the Mission list under Settings>Online>Jobs>Rockstar Created>Missions.
That was pretty much the only thing I was super frustrated with, and had Rockstar bothered to put in 10 seconds to explain "hey you can do missions that people actually want to play with this button in the phone", maybe I'd be Level 50 by now.