I'll second the vote for the GoPro. I've worked on a number of reality shows that use these cameras for close up work in hazardous situations (like right next to the watermelon that's getting blasted with a shotgun...) because it's HD, it's compact and hide-able, and for the price, more 'expendable' than an XDCAM.
As for the top of the goal...the "naked" version is about the same size as a pack of cigarettes. A consideration might be one at each upper corner, trained on the center...two perspectives. Not sure if your budget allows. But, based on the goals I've seen, I think it'd be just fine on the upper crosspiece, small enough so that it's not distracting. I'd safety chain it so it doesn't bean the keeper if a ball hits it square on and knocks it off the goal. :)
I've had VERY good luck with these in terms of image quality, and the wide angle coverage is really spectacular. I prefer wide, though, YMMV.
Battery life...that's another issue you may have. I know that there's a battery pack that slaps onto the back, making it a bit thicker--maybe the thickness of TWO packs of cigarettes? I'd highly recommend that so you can ensure a full 90 min+ of coverage without having to worry.