There are a whole bunch of factors involved here which I'll get to in a moment, but let me start off by saying that unless storage space is absolutely critical, never, ever, ever, and I do mean never mess with your original images. If you're shooting in .jpg, then make a copy of them and work with that. If you're shooting RAW, make your initial adjustments, save as .tif or .jpg and work from there.
Anyway, to get into this a little more deeply, "image size" has a number of different meanings. First off there's the size in memory which is what I think you're concerned about. If you're shooting .jpg, a 6mp camera will generally turn in best quality .jpgs that are about 3-5 Mb in size and a 12mp camera will produce 6-8Mb large/fine .jpgs. RAW files are significantly larger (20+Mb for a 12Mp camera) but contain much more information, and allow you greater lattitude in your post-processing.
Display dimensions (That's the 3168x2376 you mentioned in your post) have little relation to size in memory, but everything to do with the size the image is displayed at on your computer or printed at. That dimension rempresents the number of pixels in the image, that is, it was taken with a camera whose sensor has a sensor 3,168 pixels wide, and 2,376 pixels high.
There are two different, and often confused (and somewhat interchangable) units of measurement that relate to display size. One is Pixels Per Inch (PPI) and the other is Dots Per Inch (DPI). PPI relates to how the image is displayed on your computer screen and DPI to how the quality of a printed image. Typically .jpg images are interpreted as 75PPI, while photo-quality printing is done at 300DPI (although you can go as low as 240DPI and get acceptable results) which is why an image that prints out at say 8x10 will appear huge on your monitor.
So, assuming that all makes sense, here's what I do: I download all of my RAW images (I always shoot RAW) to my hard drive, go through and weed out any immediate dogs. Then I go through a second time and mark all those that I think are worth post-processing. Now I fire up my RAW handler and do my initial corrections on each image and save it as a .tif file in a separate directory. Now I run the tif files through PhotoShop and the first step I make is to crop them to whatever printed size I want (usually 8x10 or 5x7) do any other corrections and save as a .jpg in a third directory. When I crop the images, that will change their dimensions (and to a limited extent their file size). Assuming that I want an 8x10 at 300DPI, the final image size will be 2400x3000 (8x300=2400...).
Hope that helps.
Just my $00.02 worth - your milage may vary.
~John