Or can anyone suggest a good source for discount laminate flooring?

I second the suggestion for the waterhog mats. I'll post where we purchase them if I can find the link - you can get custom sizes, colors, styles, etc. LL BEAN sells them too but they are very pricey IMO. We use them around our dogs water bowls too since they are sloppy drinkers. In addition to our entry way, we also use them in the back of our SUV's in the cargo area since we travel with our Boxers. Keeps the truck nice and clean and absorbs liquids. After my dog had surgery he peed in the truck on the drive home from the vets office (post-anesthesia, if I remember correctly) and I was thankful for that waterhog mat. Not a drop of urine on my upholstery; the waterhog captured all of it, and it was easy enough to clean -- I sprayed it down with a hose and some cleaning solution, left it out to dry and no residual smell whatsoever. They're awesome mats.

No - this is a design opinion, not a technical "right or wrong" issue.

I would do exactly as you plan. I think it will look very nice that way. You'll have a rug in the entryway.