Ping steadily cycling from ~65 to ~125, back down and up again constantly

This generally points to an issue between your hardware and the Blizzard servers. Since they are not reporting any difficulties at this time, it’s likely along your route to Blizzard. Please note that other connections to different games may be working with no ping issues. To get a more direct answer, you’ll need to follow the connection troubleshooting guides and post a WinMTR.