Reddit mentions of Vaughan SH2 22-Ounce Carpenters Half Hatchet, Flame Treated Hickory Handle, 13-Inch Long.

• I am loving my mora companion with the stainless blade for $11 (amazon prime). Beats my $13 Old Hickory knife for utility and comes with it's own sheath. (Prior comment) with suggested mods.
  
  
• Disposable lighter, either Clipper (preferred, but hard to find except on Amazon) or a BIC or something. Get something translucent or white so you can see the fluid level. (prior comment about clipper lighters)
  
  
• Zippo Lighter used as a backup, spare flint storage, and the ability to use scavenged fuels. It lights in extreme cold where butane can fail. To make it practical, you really need to do the inner-tube mod. (Far North Bushcraft and Survival) Even then, expect a filling to only last 4-6 months before it evaporates. (BTW most lighter "tricks" will shorten the life of the hinge, and you still need to pay shipping one-way to get it fixed for free, buy a fidget spinner instead.)
  
  
• I'm enjoying my 40oz Ozark Trails insulated mug from Walmart (walmart.com) (~$12? I've forgotten already) The vacuum insulation is good enough to keep ice frozen overnight. You can also rehydrate ramen noodles and other dehydrated things in it by adding boiling water. While it's my constant companion, it's not ultra-light. Totally a knockoff of RTIC and Yeti, and yet it's a quality product that survived a lot of abuse. (prior Post about a year ago I guess I've had mine for at least 18 months.
  
  
• I carry an inexpensive Vaughan SH2 22-Ounce Carpenters Half Hatchet (Amazon link for photo only, buy where you wish.) I saw these on closeout at Walmart. It did not come that sharp, but no real complaints otherwise. A curved cutting edge would work better for most bushcraft duties, but flat is better if you need what amounts to a really wide chisel. It's common to find these and hatchets for sale cheap with a broken handle, this style is easy to carve a replacement for if you're into that.
  
  
• Cheap emergency only mylar "space" blankets (Amazon again), though to be honest, the original reason I bought them was to reduce solar gain through home windows (mist window with water, squeege on cut space blanket, remove before winter when you want the heat, save for next year) They're less than $2 each when you buy about 10 and they work as ground cloths, tarps, and fire reflectors. Super light weight.
  
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Buy yourself a decent hatchet. Better than a hawk for processing wood and a hatchet will have a far more substantial poll for use as a pounding implement (No striking steel on steel though!). If you are determined to have an actual hammer head, you should look into a Carpenter's Half Hatchet(aka a shingling hatchet)


In all of my time in the outdoors, I have never found any need for a pry bar. Digging sticks and wood levers? Absolutely. Pry bar? Nope.

Vaughan carpenter hatchet

https://www.amazon.com/Vaughan-22-Ounce-Carpenters-Hatchet-Treated/dp/B0002IGHAM/ref=mp_s_a_1_3?keywords=vaughan+hatchet&qid=1555884173&s=gateway&sr=8-3

Cold Steel Axe Gang are my personal favorite and a favorite of most people I know unfortunately on backorder for a while

Or the Prandi


https://www.amazon.com/Prandi-German-Style-Hatchet-PRA0308TH/dp/B0742LLJ3Q/ref=mp_s_a_1_1?crid=2RZBM9EQLOGMX&keywords=prandi+hatchet&qid=1555884296&s=gateway&sprefix=prandi&sr=8-1