Image resolution/pixel dimensions are the attributes you should probably be looking for.
To find out what numbers you should specify in your requirements, you'll need to decide on the maximum size that you'll want to print an image from the archive, then from that you can derive the minimum resolution that images in the archive should have.
For example, if you decide that the largest you'll want to print an image is the full width of an A4 page:
A4 page width in inches= ~8.27 inches
8.27 inches x 300ppi = 2481 pixels
From these numbers you could set a requirement that images submitted to the archive must have a minimum number of say 2500 pixels across.
However, there are a number of further issues that complicate matters.
Firstly (and most importantly IMO) the number of pixels that an image is made up of isn't necessarily a measure of image quality. As an example, my mobile phone and my old Canon 20D dSLR camera, both produce pictures of near identical dimensions, but the quality of those pixels is worlds apart.
Secondly, I imagine most of your images will be submitted as jpeg's so there is a question of the compression setting used. If the camera in use was set to apply heavy compression to the image before saving that'll reduce the quality of the image, whilst maintaining it's outer pixel dimensions.
This means that although you can set requirements for minimum dimensions, it's possible for images to technically meet those rules, and yet actually be of a quality lower than you need.
Thirdly, calculating the minimum image dimensions as above may be overly optimistic. Suppose you need to crop or rotate the images to fit a certain layout, that may necessitate a larger starting file to still get a good print.
Personally, if I were building an image archive for marketing use, I'd want to source images of as high a quality as possible, so the general guidance I would issue would be to make sure the camera was set to it's highest resolutions and quality settings.
Resolution wise I'd issue a guideline that images should be at least 6 Mega Pixels or have their longest side be at least 2500 pixels. (These are the numbers I'd go with, naturally they are dependant on your specific printing requirements.)