You lie, that's not a vanity. That's a (beautiful) bookcase. :p
Brian, why? Is this furniture particularly near and dear or antique or unique?
Refinishing is like major work if there is much detail. Usable furniture is cheap and plentiful, often free.
I mean trying to solder a piece of hardware you can buy for 39 cents doesn't make sense unless it's a rare or unique piece. The cost of stripper, sandpaper, steel wool, brushes, thinner, stains & finishes can add up fast.