Suggestions offered in order of priority.

A bushcraft class before time-tripping would probably be my topmost priority.

Outerwear and footwear are essential -- you mentioned clothes being available, but well-fitting and broken-in boots can easily be the difference between life and death. I tend towards waterproof boots. You'll want shelter, too, even if it's just a 2-person Heatsheet.

A larger knife would be a really good idea. Perhaps a Ritter Mk2.

A multitool. My favorite is the Leatherman Wave.

Another form of firemaking, such as a Bic or REI Storm Proof matches.

Is a handgun, or better yet, a rifle, out of the question? While a .22 makes a dandy survival rifle for many reasons, it would be my second-to-last choice (before harsh language) if I were to face hostile predators, 2- or 4-legged. Don't forget gun-cleaning tools and supplies if you have any sort of gun.

In the absence of replacement batteries, I'd likely pick a flashlight that would last longer. I'd probably pick a Quark 123^2 (I have, um, three of them).

Wiseman's _SAS Survival Handbook_ would be the book I would bring, if I could only bring one book.

A backpack? One with a hydration bladder?