The Silverstone Gantry shot looks like a relatively wide angle lens was used. The GoPro Hero 2 seems to offer 3 field of view settings down to 90 degrees although that is still pretty wide. However it may be close to what you would need for an 'approaching the gantry' shot.
The thing about the GoPros is that they have been designed to cope with jerky movement and vibration on fairly rigid mounts and I doubt many of the 'normal' cameras would deal well with such things.
I'm pretty sure that a dslr would be out. Ok for filming on the road but not really good for racing and expecially if located in an exposed location.
So you would be left with compacts (may be as well off with the GoPro Hero2) or something like the smaller interchangeable lens cameras now available, perhaps with a pancake 'standard' lens for smallness. However if fitted in an exposed location an underwater housing might be advisable for protection and suddenly the size bulks up - even assuming they are available.
The GoPro Hero 2 also offers time lapse shooting (according to the blurb) and that might be a good way to get the shots - thought slightly hit and miss depending on your ability to be in the right place at the right time!
If you are planning to trigger a snap manually ... well, that's another game although there are some compact style cameras that offer something like that sort of facility. (However I'm not sure that they would be suitable for action use on a number of counts). I would imigine you may have enough to do whilst on the track some form of automated triggering or, maybe, wireless external triggering would be better? Possible in theory but whether practical on track .... who knows? Not sure anyone has done it in a live race. (Other than as a snapshot form a video feed).