Overwatch isn’t a free to play game, it’ll release on PC/PS4/XB1 sometime in Spring 2016 for a base price of 40$. There’s also an “Origins Edition” which costs 60$ that adds new skins to select characters in the game, and other extra content for select Blizzard games.
Sadly beta invitations aren’t in the pre-purchase option for Overwatch. Check out the game’s store page here.