Your hardwood floors in your kitchen are gorgeous! Have you considered placing those in your family room? I know it costs more, upfront, to install hardwood, but...carpet has gotten to the point where it's pretty expensive, itself, and it's an expense that keeps coming up again and again. Carpet, the way it's currently made (and, imo, despite any claims to the contrary made by carpet manufacturers), really doesn't look nice/last longer than a few years. From what I've seen, most carpeting in most homes then spends several additional years on the floor, looking like it needs to be replaced, before it actually gets replaced. This seems to be especially true in high-use areas like a family room. Anyway, if you can do it, I'd extend the hardwood from your kitchen into the family room. Hardwood can last a lot longer than carpet. If you can't do hardwood, I also like the second from the top in the row you selected.

@veggiegardnr - Carpet will last a long time as long as you clean it regularly. No, you don't have to have it professionally cleaned yearly. Vacuuming your carpet will stretch the life of the carpet. Keeping dirt out of the fibers is your goal, just like sweeping a wood or tile floor. Very simple. An upgraded pad with a moisture barrier is also a plus. If the kids spill something or a pet has an accident, the moisture barrier keeps the stain from soaking into the pad making the area easier for clean up. All stains reside in the pad. Example; Apartment complexes... You rent an apartment and within a couple weeks you notice huge stains in the living room and bed rooms. The carpet was cleaned before you moved in...but the stain resides in the pad. Carpet cleaners only clean the surface of the carpet. There goes your deposit.
I have a 15 yr old residential grade carpet in our showroom that gets vacuumed once a week and has been professionally cleaned 3 times. We have very high traffic and it still looks as if it were installed yesterday.

Yes, hardwood or tile will last longer but they are also much more expensive. Some people like to work with their budget and stay within the limits.

In my experience, no, carpet does not last and keeping it professionally cleaned still does not keep it looking nice for more than a few years. Perhaps I have a lower tolerance for carpet that's starting to look ratty vs other people.

So far as that waterproof pad... I had new carpets (the smart strand) installed in the bedrooms in my last house. Shortly thereafter, my cat got sick and she had three accidents on the carpet (urine). All that waterproof pad did was to allow the urine to spread out in a larger area than it would have if we'd had a regular pad underneath. Three spots that would have been small turned into three spread out spots. It was awful. We had two different professional cleaners to clean the carpet in that bedroom. They couldn't get the urine out. It smelled horribly. Both came twice. We ended up lifting up the carpet and cleaning it from the back side. The urine had spread out into large spots because of that pad. I'd never have a moisture proof pad again. If we'd had regular pad, I think it would have been easier to clean (and just replace that section of pad, if we needed to).

The carpets in my last house needed to be replaced three times in 11 years. We replaced them once when we moved in, about half way through when we lived there and, then, they were ready to be replaced again when we sold the house. The carpet was just as expensive, per sq ft, as the hard flooring that we put in the rest of the house, when we bought the house. The hard flooring looked pristine when we moved out. The carpets needed to be replaced, again. Carpet can be (but it isn't always) less expensive up front. But, the expense of replacing it comes back again and again, sooner than many people realize. There are also hard flooring options that are the same price, or less, per sq ft. My in-laws paid the same price per sq ft for their hardwood floors as they did for the carpets in their bedrooms. They put in hardwood everywhere except the bedrooms. Then, when they moved, they had to replace the carpets and they were shocked at how expensive it was to replace the carpets.

We are two adults who are clean in our home and the only pet accidents we had the entire time we were in our last home were the ones I mentioned previously, when my cat got sick. We vacuumed about 4-5 times per week. The carpets didn't look dirty, but they had wear patterns and just looked ratty and old. Of course, when they are taken up, it's always obvious that carpets ARE dirty. They simply are not able to be kept clean like hard floors. Vacuuming and professional cleaning will not keep them as clean as you can keep a hard floor.

I'll admit it. I don't like carpet. I'll never willingly have it again. I hesitated to say anything on this thread, but, when I saw those beautiful hardwood floors I just wanted to say that I'd do that, if possible. I thought I'd mention it because maybe it wasn't something the op had considered. Anyway, sorry. I realize this probably isn't what the homeowner was looking to hear, so I will try to avoid saying anything else.