Fishing requires much time and does not yield much profit until its later levels. Unless you enjoy it for its own sake, avoid seriously delving into fishing until your level limit. It is not a bad idea to do a little when starting out a new character on a new server, though - the gray items you fish up sell for good money to a starter, which can help you out with your other tradeskills.
As late as possible. Early on, you’ll want to follow the missions in Battle for Azeroth right up until you get the option to send a follower on a two-hour long quest. As soon as you get there, stop doing the War Campaign missions. You can come back to them once you have reached something like 119 and a half and finish leveling with those if you want. If you don’t use these missions to cap off your leveling journey, then they’re the first thing you’ll want to do once you reach max level.