What nominal lumber size is 11/16

You won't want to use pressure treated wood in any application where people will be touching the wood often, especially children. Cedar is a good wood for outdoor applications, and is often used in playhouses and swing sets. If you've got really deep pockets, Teak is a very good choice for outdoor applications. Teak is often used in higher end patio furniture, because is is very low maintenance and stands up well to weather, due to its high oil content much like cedar.

You could probably get away with any type of wood (even pine), but you'd have to seal it yearly and replace pieces if they did start to rot.

I used poplar in my home, it is cheap compared to other off the shelf materials. It took stain very well, but a word of caution, the heartwood of poplar is green, takes stain well, and when it ages it turns a nice shade of brown from UV exposure. The sapwood is the bad guy here, it is really light in color, as soaks up the stain, so much so, that if there are any dark pigments that make up the stain color, for some reason the sapwood really accentuates the dark color, when on the green heartwood it responds differently to the color of stain being applied, so much it looks like 2 different stains are being used. This problem was not evident when I built my home in 1989, poplar then was pretty much all heartwood. My remodel that I finished last year proved different using poplar. Poplar today has a lot more sapwood, and just a little heartwood which makes it difficult to stain evenly. Maple has the same problem but for a different reason, but the fix is the same. There are "wood conditioners" out there that are applied first to soak up into the softwoods or "curly grain" like maple that will let the stain soak in evenly, at least more evenly than without the conditioner. This may be the simplest fix for the problem, though there are other ways to get past the problems, but they include a lot of trial and error- time consuming.