I think it is awesome to give a piece of furniture a new life. It is sometimes a bit daunting to take a paint brush to a piece made from genuine old timber but if you are going to get many more years of life and enjoyment out of it I think it is better than dumping it. I believe it shows your love. jbof4 I started with a heat gun to remove most of the many layers of paint, (some are easier than others to strip this way). Then I used an orbital sander and sanded and sanded and sanded. You might also try liquid paint stripper although I find this very messy. I believe you can also get them professionally stripped. Good luck with the resurrection, go for it what have you got to lose.

Medicine cabinets have come along way in recent years. The best option is to get a frameless style and integrate it into a wall of mirror. You can mount sconces thru the mirror on either side of the cabinet. If you have walls on either side of the sink, you can put the cabinets to the side, integrated into mirror again. If you have an open wall in your bath, yo can get an extra tall medicine cabinet to hold loads of stuff. There are loads more on houzz photos. Just search medicine cabinet. Sometimes you have to hunt for the cabinet because they are so well integrated. Robern makes some of the best frameless styles, but there are a ton of others on faucetdirect.com. Many even come with integrated lighting for a very modern look.

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I'd do the island black but not the overhead cabinets.