Good news: You can use Fireworks to determine the print resolutions of your images!
Open each image in Fireworks and choose Modify > Canvas > Image Size... to open the Image Size dialog. Now, be sure that Resample Image is unchecked. Under Print Size, choose centimeters as units, and then enter one or both dimensions of your intended print output size. The Resolution will update according to the print size that you specify.
Recommended print resolutions might typically range from 180 to 300ppi. However, the larger the print, the lower the resolution needed, as a larger print invites a greater viewing distance. (One source that I have lists 300ppi as 'extra sharp', 200ppi as 'sharp', 150ppi as 'moderate', and 110ppi as 'soft'.) The best thing to do is to run some test prints yourself, or have a talk with your printer for recommendations. You can increase the pixel resolution of your images, but it won't increase the resolution of the image subject (e.g, the cat)—that said, when enlarging/resampling images, Bicubic Smoother is typically recommended; when reducing images, try Bicubic Sharper. You could also apply Sharpening to try to increase the apparent sharpness of a soft image, which may or may not be helpful.
For a print project, I'd recommend Illustrator; otherwise, Photoshop. Both applications are set up for print and will allow you to save a file that includes vector logos or text, for a sharper-looking output than Fireworks.
Finally, if worse comes to worst, you may want to substitute stock photography for one or more of your personal pet photos. (Or you could try taking some new photos.) Or here's an idea: Hook up with a local pet photographer to take some custom, high-end images—perhaps in exchange for in-store promotion, etc.
FOLLOW-UP: After re-reading your question, I wanted to add one thing: If you're resizing an image in the context of a layout in Photoshop or Fireworks, you're best off defining the image as a Smart Object (in Photoshop) or a Symbol (in Fireworks) before resizing it. This will preserve the image's native resolution, allowing you to scale it up or down in size, without any loss of image quality. If using Illustrator, the image file will be linked or embedded, and its native resolution will be preserved by default.
Thanks a bunch for the elaborative answer! That last part:
"FOLLOW-UP: After re-reading your question, I wanted to add one thing: If you're resizing an image in the context of a layout in Photoshop or Fireworks, you're best off defining the image as a Smart Object (in Photoshop) or a Symbol (in Fireworks) before resizing it. This will preserve the image's native resolution, allowing you to scale it up or down in size, without any loss of image quality. If using Illustrator, the image file will be linked or embedded, and its native resolution will be preserved by default."
was exactly what I was looking for.
I tried what you said and entered the true print size of the cat (which is my own photo, as are the others, they are just not shot now for the purpose of this project) which showed that the print resolution would be 83 dpi, which I realize is very low. I just confirmed with my girl friend that one of the plates (there will be six of them) are located just next to the ramp up to the door, so that plate will be viewable from approx half a meters distance, which is closer than I previously thought. That said, 83 dpi is probably too low. Follow up question: How much can an image be upscaled with reasonable outcome? I figure I would need ~130-140 dpi. Is that possible or should I just throw away the image and go for new ones? From your point of view, yes of course =), it's just that this is by far the best image I have if I disregard the low resolution.
Thanks again for the helpful answer!
I think you need to try printing the images that you're concerned about, and see for yourself if you like the results. (I'd just try printing using an inexpensive printing source—a desktop printer, a local copy shop, the library, etc.)
You can enlarge and resample the image (e.g. using Bicubic Smoother), but this often just adds pixels without improving image quality. In my own experiments, it hasn't been needed. However, if the image looks pixelated or aliased when printed, then you'd definitely want to do this. Either way, it doesn't hurt to see for yourself.
Previously, I'd suggested that you could try Sharpening a soft-looking image. If it were stylistically appropriate, you could also go the other direction and try adding a soft-focus or contrast-glow effect. In fact, a dramatic processing effect of any kind might help to mask the lack of image quality in a single photo, or help to unify photos of differing resolutions. It's up to you whether it'd be the right choice for the project, though.