Honestly, I don't see the Browns truly going all in for Mariota. If they can get away with giving 12 and some combination of later picks this year and a relatively high pick next year, maybe they pull the trigger. However; I would be surprised if they used both 12 and 19 in a package for Mariota.
Now I can see them using 12 or 19 but not both in acquiring a current starting QB like Bradford, Rivers or someone else. It all depends on what Tennessee wants in return for the #2 pick. I'm not sure the Browns have any control over that process, it's really in the Titan's hands how that goes down.
I think the more likely scenario is they stay at 12 and select either Parker or Shelton, whoever is on the board. At 19, if one of the premier pass rushers (Dupree, Ray, Beasley) are there I think they pull the trigger. I think they stay away from Randy Gregory. If not, they very well could trade down a few slots and pick up either an Eddie Goldman if they took Parker at 12 or a Perriman/Strong/Devin Smith if they took Shelton at 12.