If I wanted a machine to drive my guns to the fight, I'd stick em on a plane or a tank or a boat. When I see a jet holding a sword, or a tank driven by one teenager as if it were his own body, or a legged vehicle walking over anything but the shittiest terrain, all I can think of is "oh GOD, our BUDGET...!"
I voted for Evangelion, since you're not really operating a military weapon designed for fighting, so much as you're being drilled into the spinal cord of a dead alien that acts out your dreams for reasons nobody understands. The criteria aren't really the same. EVA will waste everything else on the battlefield, but powering the thing costs more than the army I destroyed, so I haven't really won here, but against another alien, an AT field is the only thing that works. The machine is apt for the role it's being used for. I like apt things.
Otherwise, I'd go with Metal Gear Rex. It's supposed to carry nukes wherever you feel like and then fire them without anyone knowing, which is a decent enough reason to wave off the legs + heavy armor + tiny crew combo that I feel defines the viability problems with mecha.
Also, MGS4, you know the part. Liquid had to tiptoe around in this thing cause he actually meant to use it again afterward, but I get to shoulder through catwalks and knee buildings in the building groin cause I already know Rex is gonna be a smoking pile once I'm done with it. The cost is tremendous.