What types of materials should I consider when designing a bench

The sand will definitely not absorb/release enough water if it's ever open to the rain. If your box doesn't drain, you'll have a small pond (as we do if we ever forget to put the lid on).

Your landscape fabric idea sounds pretty good. I'd just build that on top of decking slats or something like Trex (which might be perfect for this). Some gaps between the slats will allow drainage. Look into what the decking material is treated with. I'm in the camp that believes that the fears of CCA pressure treated wood are overblown, but even I probably wouldn't use it in a sandbox for a three year old.

Keep in mind regarding sliding it around: Sand is heavy, especially when damp (100-130 pounds per cubic foot). We have a pretty small plastic sandbox in our yard and I can't move it without dumping the sand first (but then "small" to me is something that holds three boys :D and I'm sliding across grass). You might want to think about furniture glides if you can find something that will slide reasonably on your deck, or even castors. Those will require that your base be much more rigid of course.

I usually build people houses, but have built a dog house or two. My research says that the size should be adjusted to the size of dog. It wants to be just big enough for the dog to lay down stretched out, and not too tall. A raised insulated floor is good. The reason for this is that the only heat source is the dog's body heat and too big a house will be too cold in winter. Of course, it should be insulated and have a safe sheathing on the interior to cover the insulation. It should also have some type of flap door that the dog can easily pass through, but will reasonably seal the opening from the elements. I have seen several books with designs and decors for your pet's condo at building materials stores and book stores online. Don't forget to put it's name on a plaque over the door!

PS: If the weather is really bad, let the poor thing indoors, have a heart.