What I don’t like about area rugs is how the edges always seem to curl up under the to-and-fro of moving chair legs. Danger of tripping over them.
I’m in the hardwood floor camp, and proud of it.
My house is c.1917. When I bought it, it had fugly wall-to-all carpeting on the first floor. One of my first tasks before moving in was to remove the carpeting. The dirt and grime of many years was suddenly revealed, requiring the purchase of face masks. The previous owner had cats, and stains were visible throughout the carpet. The underliner (is that what it is called?) had deteriorated, and fell apart as soon as I touched it. In general, a respiratory nightmare. It is my personal (probably paranoid) opinion that wall-to-wall carpeting contributes to asthma in children.
After removing the carpeting, I was amazed at the quality of the floor installation. It was installed in concentric squares. It was awhile before I could have it refinished, so I covered it with removable rugs that could be cleaned professionally. After it was finished, it was just amazing. The rooms just lit up, and the character was so much richer.
I know that it is expensive to install new hardwood flooring, but I believe that it pays for itself in the end. I work for an engineering firm with architects. I have been in meetings where the architects advise the clients that wall-to-wall carpeting can be replaced (x) times before the cost equals that of (more expensive) flooring. But once the carpeting is down, and furniture in place, it is just a PITA to rip it up and replace it. My suggestion would be to go for the hardwood floors, and then cover them, if desired, with good rugs.
Yes to the polyurethane. There seem to be two types (someone with more knowlege can jump in here). There are the water soluble ones which dry crystal clear, but are less resistant to wear. The advantage to these is that you can repair small areas by yourself and still have it look good. Then there are the solvent based ones (may not be available in some states like California due to VOC air quality concerns). These can yellow overtime (although not very much), but are much more resistant to wear. The disadvantage is that you have to be good to repair small areas and have it blend in.
Dust mites. Fleas, pee, poop (if you have pets). Anything you track in on your shoes. Food fragments.
How do you feel about that nookie now? Germophobes meet Thursday nights, down the hall. Happy to help. 
I despise carpeting. I can’t wait until I can afford hardwood. Fortunately, I have a very small house so it won’t be outrageously expensive. I may even keep the bedrooms carpeted to cut down the expense even more.