Hello,
I want to play wow classic with my son. I was wondering what is the best way to create a 2nd battle.net account so we can both play at the same time. Also will we be able to switch between battle.net accounts on the same computer without messing things up?
The best way to do this would be to create a new Blizzard account under your name. Your son can use your Blizzard account until they’re older, at which point the account can be transferred over to them if desired 
Once you have a second Blizzard account setup, setting up a new WoW account can be done from your Account Management page under the “Games & Subscription” section.
When you have a new WoW account created, setting up a subscription for that account will give it access to current WoW up to level 110 (Legion expansion), AND give access to WoW Classic.
Switching between your Blizzard accounts on the same computer won’t cause any issues