Looks like the competitive scene is going to be fairly active for this game, at least initially. For ANZ there have already been 2 tournaments run (in the closed and open beta), with 17 teams competing in the most recent one. At the moment there seems to be a few options going forward.
JAM-Stah Overwatch Weekly - Starting Thur May 26th (Yes two days after launch). From what I can see this will be a single night tournament, starting at 7pm each Thursday. Some matches streamed and minor prize money on offer (free entry, max of 32 teams with 9 currently signed up).Winterwatch - Starting Sat June 4th 10am. This tournament will be held over 3 weeks, but would require playing during the day on either Sat or Sun. Similar setup to the JAM-Stah one.
Cybergamer - has started ladder sign-ups, with 20 teams already registering an interest. This would require a longer term commitment, with a ladder often running for a number of months.
We'll see how much interest this game gets internally, however there definitely seems to be a number of options if we end up going down the competitive route for this game.