Outdoor kids playset - type of lumber use/look for
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.