I would go with either the Kindle Fire, the Acer, or the Lenovo IdeaPad. However, if the 13 year old would like a camera on the tablet, then don't get the Kindle Fire since it has no cameras. I know the Lenovo has both a front and rear camera and is the same price as the Kindle Fire.
Unless one roots the Kindle or the Nook, I think, they only have access to either Amazon's or B&N"s app stores. The Acer and Lenovo have access to the Android Market. One can also install the Kindle and Nook readers on these to read their books and such.