Actually, the best thing is to format a new (or used) memory card in the camera itself. The possibility exists that the manufacturer of the card did not format it, or formatted it slightly differently than the camera 'expects' it to be, etc. It's likely, too, that each camera manufacturer has some proprietary differences in formatting cards. As are result, if using a card in different cameras, it should be formatted by the 'new' (to it) camera. While formatting on your computer would usually work, again, minor differences might cause unexpected results in your camera...such as only partially usable, partially readable, etc. I had just such a difference between my older Windows XP computer and a Canon 30D after formatting the card on my computer.
I always copy the images from the card directly to my computer, and immediately make another copy onto a USB thumb drive as a backup. As there is usually some time between shoots, I don't re-format the card until I've completed all post-processing for that shoot. Then, and only then, will I format the card in the camera, erasing all images. And yes, for all practical purposes, the images ARE gone once formatted, although recovery software can get most, maybe all, back. But that's a very shaky proposition and should only be used as a last resort.
I also have multiple memory cards. That way, if I have to go do another shoot before finishing with the 1st one, I pop in a different memory card.