Without going to the lengths documented in the Chain Waxing thread, just what is the best way to make my chain nice and shiny?
I used an eco-degreaser in the Park Tool chain cleaner, and superficially it looked like new again. However, after adding a dry lube (Finish Line) to the links, it didn’t take long before I had grey gunk working its way out, over my fingers and the rest of the drivetrain. 
Any tips appreciated.
Really like this lube. A little bit goes a LONG WAY! Just a small drop on each link, let it penetrate a minute or so then run it thru a clean rag.
I’ve tried Finish Line before with similar results to yours and found my drivetrain gunked up just as badly.
For waxing? Do a mineral spirits bath a couple times. For wet lube degreaser in a shaker or ultrasonic is ‘good enough’.
Clean it the way this tells you to clean it.
Not sure I’ll clean a chain the “old way” (which was a degreaser and sometimes one of those funky chain washer things) ever again. The jars of spirits work really well, and you can filter and recycle the spirits.
That is a very thorough guide – cheers!