For your requirements there are only a few options: Tile, vinyl plank, finished concrete. I would only recommend tile or concrete in warm/hot locations. Florida, California, Arizona, etc do very well with these "cold" floors. Other than that, vinyl is where you will end up.

It is the "water proof" that is throwing you into turmoil. There are very few "water proof" products out there. The heavy wear from dogs and "dirt" being tracked in from outside will also reduce your options.

Personally I'm a fan of water proof laminate. Aquaguard has a LONG history of great wear + water proof + great looking product for a great price. It is different from LVP (Luxury Vinyl Plank) as it does not contain vinyl (PVC). The core is NOT made of wood. It is a composite core product (actually it is a black "plastic" looking core).

And like ALL laminates it is ALLOWED to have UNDERLAY used. That is MUCH different from most vinyl plank products. Very few LVP products allow underlay. Traditionally they HAVE to be installed right over plywood or concrete.

If you are looking at LVP or water proof laminate, you can often use them on the stairs. Traditionally the main floor (the public areas) are to match (complemented by) the stairs. In other words, if someone is visiting and they are on the main floor, they can look at the stairs without wondering why on EARTH are they different from the rest of the flooring they are standing on.

Once you get to the TOP of the stairs (usually the private areas reserved for family members) you can have whatever your heart desires. Of course this presumes the lower level cannot see the upper level flooring choice....you get the idea.

Anyway, water proof laminate (like Aquaguard) opens up the possibility for flooring. But all of this depends on where you live and the value of your home. As for solid strand woven bamboo, it CAN BE a great product...so long as you stick with the BIG TICKET products. I don't trust any bamboo that is LESS than $9/sf. And the REALLY good stuff comes in around $15/sf (before install). And bamboo is PICKY! After that it is TRICKY. And then just for good measure, it is picky.

Bamboo requires EXCELLENT humidity control. If you already have a whole-home humidifier/dehumidifier (depends on where you live) that can keep TIGHT humidity control at ALL TIMES during the year (as in nothing more than a 10% swing in humidity in a year), you are welcome to look at high-end bamboo. If you are researching $5/sf bamboo, then I suggest you look at something else. You won't get what you need out of bamboo at that price range.

A laminate floor is a product with a PHOTOGRAPH sitting on top. That photo will depict something like wood, stone, tile or even carpet (yes...I've seen it).

The Aquaguard Engineered bamboo has ACTUAL BAMBOO sitting on the top of the plank...not a photo. I'm reading the installation instructions (and warranty doc) and the bamboo installation has a very TIGHT temperature and humidity range. So tight, that you MUST HAVE access to humidity control that you can change with the tough of a button (electronic humidistat that is attached to the home's HVAC system).

https://www.flooranddecor.com/bamboo-wood/tasika-hand-scraped-wire-brushed-water-resistant-stranded-engineered-bamboo-100500081.html#start=15

https://www.flooranddecor.com/bamboo-wood/tasika-hand-scraped-wire-brushed-water-resistant-stranded-engineered-bamboo-100500081.html

Before you do ANYTHING with the bamboo, you will need to look at your home's HVAC system. I am NOT kidding about the TIGHT humidity control. Your home MUST SIT between 40%-55% humidity at all times. And the temperature range is the TIGHTEST I have ever seen for a floating floor.

The bamboo is 7mm thick yet it needs 1 cm (10mm) of expansion at all walls. That tells me this thing moves MUCH MORE than you would think. That is also confirmed by the humidity control and the temperature control. You need to live in a hermetically sealed home to get the bamboo to work.

To be clear, most bamboo is touchy to live with. This stuff is DRAMATICALLY different from the "normally picky" bamboo. I would guess the bamboo would delaminate under 'normal' USA living conditions. I know the core for Aquaguard is quite rigid and doesn't do much...but the BAMBOO is quite dynamic. That means they have paired two items that don't work well together. And guess what? They don't work well together (surprise surprise).

It's your call. I wouldn't touch this with a 39 1/2 ft pole (to quote Dr. Seuss).