Here is how i would do it....
Make a TV called "Categories"
Set the Input Type to "DropDown List Menu"
In Input Value Options add your categories.. so something along the lines of "Cats||Dogs||Uncategorized"
I would set your Default Value to "Uncategorized"
Make sure you add it to the template that you want categories to attach too
To list the pages with that category put in a code similar to this to only show pages about "Dogs"
[[Ditto? &startID=`44` &summarize=`50` &total=`50` &tpl=`category-tpl` &filter=`Categories,Dogs,=`]]
Change the &startID to where you keep all the pages that have categories.
You may want to bring the summarize or total down a bit.
The &tpl is the template you want to use for how you list the pages you use.
This method allows you to have all your pages in one folder.. you could also add multiple categories (really more like tags at this point) by setting the Input Type to "Listbox (Multi-Select)" in case you had a few page about kittens and puppies in a basket and wanted a list those on a page together as well as in their respective category.