Hi Chevre and welcome to the forum
My knowledge of precisely what to do with washed rind cheeses is virtually nil, so when I made my first one, I was winging it. That was a taleggio.
And yes, I just used the brine, and kept it in the frig and used a little bit each time I washed, thowing out what remained after the washing as it does get contaminated. Not sure about the wine/beer, but it sure sound a great idea and one I might try myself one of these days.
since then, I have done a couple more and used the same procedure, though one cheese (I forget which) required a 3% brine solution, so I made it up especially for that cheese. Otherwise, I use the one I normally use for other cheeses, 20% or thereabouts.
Best of luck with it