I know you wanted serious answers EP so I'm sorry. I'd bring Dora the explorer because that bitch has everything in that backpack! Sorry again but is never have another chance to bust that out.
Oh no, that counts! One thing that's about as essential as a shelter in this context is a sense of humor. If you don't learn to laugh at some of the stuff that goes down while you and your fellow domesticated primates try to answer the Call of the Wild (as opposed to the much more commonly-answered Call of Nature) then your wilderness experience will merely be a shortcut to madness.
You know, I keep forgetting to mention that to truly live in full survival, with no manufactured tools or equipment (directly off the land), we won't be in the woods or rather we won't generally be very far inside of a forest and if we do go deep, it won't be very often. Relatively speaking, there's not much besides wood in the deep woods; all the hard-core bio-action is in the transition areas between
biomes, such as where grasslands meet forests or coastlines and places like that.
That's why all the brushy dog-hair thickets where nice fertile land used to be annoy me so much; those are the places where we'll have to go if we're living off the land full-time, and all agricultural and suburban land will turn into briar-infested, nearly impenetrable thickets real fast once internal combustion is silenced forever. That's one reason I strongly advocate having a Woodsman's Pal machete in the bug-out kit; it'll be a true life saver once there's no more landscape maintenance or bush-hogging going on.
And while it might be a great thing to do while living in an intact and thriving civilization, hiking the Appalachian Trail is also the worst possible route for traveling on foot (or any other way for that matter) from the Southeast to the Northeast if one is merely trying to get from point A to point B and not be someone who hikes the AT. So interestingly enough, it might not be hitting the woods that's the ideal place to go, it might be the suburbs! Once the 'burbs depopulate from lack of logistical support, they might be good places to go hide out as they are often in fertile or transition areas (or will quickly become new biomes or transition areas as all the formerly carefully maintained, landscaped land goes wild). Many foot trails are similarly located in beautiful but inconvenient locations because all the gentle hills with easy grades and fertile land and good water where livin' is easy were claimed and fenced and defended a loooooong time ago.