Determined this is what I want to use around the house to cut kindling and also to display.  I'd love a Damascus blade but don't believe I can get one within my budget of ~$150.00.  
I will not be using this as a throwing hatchet.  I've got some cheap rocks if I want to throw something.

Wants:  Handle with a curve, black "rough" (forged) head, something worth throwing on the wall when I'm done, darker wood handle.

GO!

Geansfors Bruks Swedish Carving axe is my favorite but it’s a little over your price.
Look on Pragis Northwoods Outfitters
https://www.boundarywaterscatalog.com/gransfors-bruks-inc/gransfors-bruks-swedish-carving-axe-5758

@Urimaginaryfrnd. Sent IM

https://www.amazon.com/Hultafors-840066-008-SV-Hatchet/dp/B001J2FIM8

OP, with your stated purpose in mind, do yourself a favor and check out the Husqvarna line of axes! They are Swedish made and I actually like the 2 I have over the much more expensive Gransfors Bruk line.

Husqvarna Forestry Tools

i like my husky carpenter's axe.

gave $50 for it out the door.  very solid but probably too big for OP's uses.

I’ve done some research on this company in the past.  Not easy to get currently, if not in a rush may look into them.
I was looking at the forestry axe,  the link below is to one of their hatchets.

https://www.gransforsbruk.com/en/product/gransfors-wildlife-hatchet/

I've got 30~40 axes and hatchets.  Which is best really depends on your actual use.  The multi-edged spike hawk might be good for puncturing a 55-gallon barrel of diesel but, is horribly impractical for most people.  The Twohawks Longhunter is another option for some people and while I like mine, it is a bit of an odd choice overall.

For sheer value in a traditional axe or hatchet, Hultafor is a really solid choice out of Sweden.  Husqvarna used/uses raw forgings from either Hult Bruk or Hultafor (pre-merger) and, axes and hatchets today are not the same as those of 10~20 years ago.  That being said, they are still better than anything you will find at Home Depot or Lowes.

I would strongly recommend you review axe and hatchet options with reviews at Lamnia out of Finland!  I have at least 10 axes and a few hatchets from them and service has always been stellar for me and are highly recommended.  My latest Gransfor Bruk Outdoor Hatches was easily $30~40 cheaper than any option on this side of the Atlantic.

Ochsenkopf out of Germany are really good too but, their steel is a bit softer so, I find them better for some uses and less so for others.  This is why I own axes and hatchets from different sources out of the EU primarily.  My Iltis Axe from "Ox" is a tree felling machine!  Man does it ever cut with a vengeance.  Their "German" pattern hatchets are also a top choice.  Stihl USA sells rebranded Ochsenkopf options and I find their ~$35MSRP options a real steal!  For ~$100 you can get the German Pattern Hatchet, the splitting axe, and the larger felling axe.  Huge value there IMHO!

So, coming full circle, on the cheap end Stihl USA for an Ochsenkopf rebranded option.

For something a little more specialized and optimized, if you know what you need, Hultafor!

Premium options are Gransfor Bruk and Hult Bruk (they have two lines, one with a lot of hand fitting for a real premium example).  Both are specialist tools and perform exceptionally well.

Ochsenkopf is a bit of a different option and philosophy.  Not better or worse, just a different approach.  In general, they are at the upper mid-range to premium price range.

I have a Council Tool Hudson Bay Belt Hatchet and a Hults Bruk Almike.

The Sweedish Carving Axe  has a different feel in the hand than anything else I have found. It is an absolute pleasure to use.

I picked up an Estwing hatchet when I was in home depot one day.  Works great.

Not Damascus.

$35

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