If at all possible to shoot one down, we would. Humanity as a whole, not idealistic dreamers. I'd be curious for answers, sure, but the powers that be would too. They'd want answers without risk, answers in a carefully controlled environment without repercussion.
I disagree.
I think you're far too quick to lump all of humanity into one category. Just like most sci-fi is. You're right, a lot of sci-fi and fiction in general is escapism, catharsis, a lot of nasty psychological needs that go unfulfilled otherwise. But do you really not think there is not a substantial enough portion of humanity that would be disgusted by the idea of their governments destroying any alien visitors?
At worst, I can envision a Cold War-type scenario, where they are loath to give us motive and information, we are loath to trust them, and they kind of just sit in orbit until some diplomatic solution can be reached or all-out war is attained. But I think any race who is as vibrantly different as our own, has had to cope with differing opinions throughout history, and has survived despite those disagreements and arguments that may or may not have evolved into all-our war, would have the patience and diplomatic ability to communicate with us.
Also, where are you getting this "combat experience" thing? If aliens are real, I have a feeling they'd be very unlike anything we could imagine or expect, so other than the Cold War scenario, the worst thing would be that we simply can't communicate with them at all.
But I guess my point is, you forget that the powers-at-be are elected, in most of the first world countries, by the people they lead, and I generally believe people long to understand, belong, and learn. Yeah, we'd be scared ****less at first, but I think humanity has proven, time and time again, that it can overcome fear in search of something greater.