You can't do it from the NRC app on the watch .. you need to select the playlist from the Music app on the watch. You can then double click the Digital Crown to switch between the Music app and the NRC app. Both can run at the same time.
In stand-alone mode (i.e. leaving the phone behind) you can play whatever playlist you'd already synced to the watch from your phone. (Watch app >> Music >> Synced Music)
Obviously, you're not going to be streaming any music without your phone.