Ok,
Please don't use the Photoshop slice function, barely anyone in this business uses that function, for the main fact you suggested above, it creates so many images, most are useless and you don't even need them, so please don't use the slice option.
I will tell you my technique (which may differ from other people) but when in photoshop, I use the crop function, and crop the individual image, and once cropped I then save this as whatever format is needed, and save it into my directory.
Then I CTRL & Z (Undo) and then I go back to the original again, and on this I do the same again, crop another piece of the website, and do the same saving as above.
Then you can begin the joys of coding
