You can do any of the above and some folks who really want to try brand new juices with a brand new coil may often take the coil out and put it in a little zip lock baggy and attach it to the bottle of juice they were vaping with. That can kind of work out provided you don't have say, 30 juices to hand that you want to try.
I personally find just vaping through and/or a quick soak in vodka to remove flavor residue works perfectly well. I do try to keep my flavor profiles similar, I mean I'm not going to try to go from a chocolate sort of juice to a lemon one, that would be a half a tank of horror that I might personally want to avoid. But, they're all reasonable strategies and etc.
Anna