Here’s a simplified explanation: Let’s assume that 200 DPI (dots per inch, or d/in) is what the machines used for printing at Cafepress are physically able to do. They can print 200 tiny dots (in any desired colour) on one inch of paper, t-shirt, whatever.
On the other hand, your images are measured in pixels. If you want to get the best possible result, you’ll want to resize your picture so that one pixel corresponds to exactly one dot being printed (thereby printing at the printer’s “ideal DPI setting”).
To do that, you’ll have to know the exact size of the printing area. For the “Ash Grey T-Shirt” (no. 5 on your specs list) this area is 10 inches by 10 inches (on the front). To calculate the best image size in pixels, just multiply the width of 10 in by 200 d/in and you get 2000 dots. Since we said we want one pixel to correspond to one dot, that means our image has to be 2000 pixels wide. Do the same for the height and you get a required image size of 2000 pixels by 2000 pixels. Of course, that’s exactly what’s written in the specs (image size at ideal dpi).
So now we know you’ll need a 2000 x 2000 pixels image to print on a 10 x 10 inch area with 200 dpi. At this point, you can completely forget about the dpi setting and simply resize/crop your image accordingly so that it ends up being 2000 pixels wide and 2000 pixels high. While many programs allow you to save a DPI value with the image (which is “for information purposes only” and doesn’t change the picture’s actual dimensions in pixels
unless you’ve set your software to measure in inches instead of pixels
), Cafepress would completely ignore this DPI value since they allow you to select the physical size of the printed image during upload, thereby determining the DPI (same math as above).
In one sentence: Get the dimensions in pixels right, forget about the DPI. If your image has the ideal image size in pixels as given in the specs, it’ll always pint at the “ideal DPI”, resulting in the best possible quality.
However, if you’re trying to use a photo which simply doesn’t have 2000 x 2000 pixels but you still want to have it printed on the entire 10 x 10 in area (instead of leaving white borders or including it in a more complex design), you’ll have to look at the DPI specs again. In this case, crop the image in order to get the required square form (let’s say your photo is 2200 x 1700: you’d crop it to 1700 x 1700). Then check if it is still within the allowed DPI range (100-300 DPI for the t-shirt): 1700 “dots” printed on 10 inches would give you 1700/10=170 DPI, which would be OK (though not as good as 200 DPI), so you could simply upload it (no need to resample it to 2000 x 2000). If it were less than 1000 x 1000 pixels (or larger than 3000 x 3000), Cafepress wouldn’t accept it (or not allow you to print it over the entire printable area, I’m not sure how exactly Cafepress works).
BTW, IfranView is a nice litte free software for resizing, cropping etc. (you can even set the DPI value which would later be ignored by Cafepress).