LOOOONG time lurker here.

Okay, so, I have a nice bucket of Amex and Chase Sapphire miles and an upcoming trip from Denver to Santiago, Chile. Naturally, I want the comfort and convenience of flying first. I have no particularly useful status with any airline.

So the question is, how do I convert these miles into a first class upgrade? I can compare outright cost on Kayak easily, but as far as I can tell, the best/only way to figure out what a mileage upgrade would cost is actually calling each airline's frequent flyer program and outright asking.

Is there a shortcut I should know about? Which airline has the best redemption in terms of points for an upgrade and how do I figure this out?

Thanks you crazy kids!