I don't think you can really make it shoot faster by pressing the button. I hold it down, but what you can do is more sweep across the target rather than point and shoot. Targets will still register. It's an old laser tag move.
I am not sure which target exactly is worth a lot, but generally the harder they are to spot, the more they are worth, so I'd think that one on the bottom of the claw would be a generally high-value target.