A card reader is different than hooking the camera up to a computer via USB or Firewire despite sharing the same type of connection. The computer treats the card reader as if it were a disk drive. When you want to transfer images from your camera, you remove your media card from the camera and insert it into the card reader. The computer will treat it as if it were a disk, and you can browse it from my computer.
If you want to keep the photos in the same format with no quality or data loss, then the card reader is definitely your best bet. It will copy the images from the camera's media card to your hard drive, but it won't make any changes to them.
I'm not familiar with Picassa or Walgreen's software, so I can't comment as to why its stripping the EXIF data from your images. Some programs do that, but I couldn't tell you why or how to turn it off.