Brass-o. You should be able to find it at your local grocer.

What a wonderful find. Kasey, I think you should use a gentle abrasive cleaner to remove any oxidation or tarnish. Look for one that is safe for metals like brass. After that, use a product like Brasso with a soft cloth to shine the hardware.

Cherry wood stain is definitely not very interesting for this piece. If the wood is nice, why cover it with paint? Perhaps re-staining it with a warmer and lighter stain would be the best solution. Something more "walnut" or "teak". A lighter color would bring to focus the hardware.

I use Bar Keepers Friend for the handles like this. Just soak them in a bowl of warm water with the Bar Keepers stuff and then buff them out with a clean towel.

You can use Brasso or a natural remedy and if that doesn't work, there are two "faux" options here: http://www.centsationalgirl.com/2012/02/brass-hardware-polishing-and-faking-it/

Your best bet is to clean up the brass and keep it original, but it's hard to tell if the pieces are quality. You might want to research the furniture brand before you do anything drastic - even cleaning the brass too harshly would damage the value. If it turns out it's nothing fancy, it would be acceptable to spray paint the handles -- you can always refinish/remove the paint later. I think an electric kelly green would look interesting with the reddish wood. Any bright color would work - yellow, pink, blue. If you are going to spray paint, make it bright and intentional.

NO, not spray paint. Brasso, like the first poster said, and a scrub to bring back the lustre. Do not paint those handles. Look at them! They're beautiful! And they look so good with that cherry.

Another vote for Brasso. But first, try hot water, dish soap and a fingernail brush.

Another good polish is Wenol. Williams Sonoma has it. But be prepared to work your fingers to the bone. You usually have to sit and polish things like this over and over. And test first. Finish can be removed with polishing. Use a soft cloth like a microfiber or flannel. If the piece is really worth the money get someone professional to restore the finish. I would strongly advise against cures like spray painting. It's so depressing to see how many pieces of furniture get ruined with a "bright and sassy" coat of paint.

I agree with Parnassus in that you should research the make of it before you do anything drastic. That being said, if it is not by a noted (collected) designer or manufacturer I would go drastic.
I would give it a nautical makeover. The wood appears in the photo to be mahogany. I would sand it down and just put a clear coat on it and replace the handles with a "rope cleat" like you would find on the deck of a sailboat.

oh, and possibly paint some or all of the case to contrast with the natural mahogany.

I prefer Simichrome polish for brass. It will remove tarnish and give the brass a beautiful shine. You only need to use a very small amount. I find it works better and faster than Brasso. I would not use Barkeepers Friend on any metal; it is abrasive and will permanently etch the metal - fine if you prefer a brushed finish but not good if you want a bright finish. And by the way Simichrome is also good for other common midcentury metal finishes such as aluminum and chrome. Here is a link to their web site. I usually can find it at antique stores and some hardware stores.
http://www.simichrome-polish.com/

This couldn't be more timely as I just got a wrought iron and brass etagere from my grandmother! Yay internet!

Nooooooo no rope cleat. I've never seen nautical-themed anything look good, even in a bathroom. Rope handles on this would look horrendous.

Brasso is your best bet on the pulls if they are actually brass and you like it.. Not a big brass fan myself but I've polished a few inherited pieces to pass on to dd (who loves it) plus a number of pieces I've refinished to gift or sell. All looked like new.

@ whoever it was who suggested staining the piece a lighter shade: It's not possible to *stain* a piece a lighter shade. Perhaps you know this, but never assume the person asking the question is so informed.

Im betting that the handles were lacquered,and a good scrubbing with thinner will shine them right up.BUT,think about getting them relacquered as brass tarnishes rather quickly and you will be forever polishng them.

If it is mahogany, it probaly dates to the early 1950s.i would clean the wood, which probably has decades of dirt and polish. It is an expensive wood and, if you look at the grain, a beautiful one. My parents had an entire bedroom set made from it.

I would not stain it walnut - it is just as dark, only yellower - and you'd be putting it on a red wood, so who knows how it would come out. Plus walnut was used in the 60s and 70.

Good luck!

Ahhhh! Don't spray paint! How tacky..

I don't really understand why you'd buy a MCM piece if you don't appreciate brass. But that's just me, I suppose.

go away, painters! that is Mahogany. note that if the finish is stripped, the wood will be a bit lighter & quite dull, so just clean w/mix of 50% murphy's oil soap/50% water in a spray bottle. spritz small area, let grime layer lift, wipe w/rag, repeat as needed, do not saturate wood. can shine brass & silver w/undiluted white polishing toothpaste (gentle enough for hygiene) to start.

Toothpaste! As mentioned by amisdottir, you can use toothpaste to clean brass and also silver. Old trick from my 80 year old grandmother and it works with no effort at all. I did that to old silver jewelery and you just rub it with your fingers, clean it with a humid cloth and it gets all shiny and new in seconds. I guess this goes for brass too?