How should I protect the metal of a power rack that's kept outdoors?
The finish shown is a type of paint - "Hammerite" is either the name, or the brand name of the most popular/first version. It's presumably on mild steel. However, any automotive paint should work (think about it) - and COULD be cheap if you have a cooperative paint shop and you don't care what color it is (ie, they can spray some excess when they spray something else, so it's not a special job where they have to mix paint and clean the spray guns just for your tiny job.) Some shops will, some shops won't - all you can do is ask.

Chrome is probably a bad idea - it's relatively expensive and the electro-plating process can increase the odds of steel cracking from hydrogen embrittlement. 

Hot dip galvanizing (zinc coating) is probably a good option if you can find a shop with a tank big enough - ask around for places that do boat trailers - covers inside and out (be sure to put in holes so it can drain out, or you'll get a tubeful of zinc and a larger than expected bill for the coating process), and is durable in weather. It only comes in one color, which changes over time from shiny silver to a dull gray. It is preferable to using galvanized steel stock to build from, because you coat the whole object after fabrication, so the welded joints are protected.

Powder coating should work fine. It may chip a bit on the top section where the weight bar sits. It comes in many colors, and is fairly tough as compared to most paints - but hard to repair if it does chip.

By far the most cost effective method usually is to do through cleaning and preparation (the key to ANY paint job lasting) and paint it yourself, using a primer for steel (zinc chromate primer, for instance) and a topcoat - then keep an eye on it and sand and repaint whenever you see signs of new rust. You could use either the mentioned oil coating or an automotive undercoating on the inside of the tubes if feeling particularly cautious.