I'm not an axe expert like some of the collectors I know. But if I wanted an axe or hatchet, you can't go wrong with an old Collins, True Temper, Kelly, Plumb, Bluegrass, Keene Kutter. Stick with the major old names and you don't have to worry about quality, tempering, etc., they will be at least decent. The old Kelly's and True Tempers would be my first choice, Kelly, True Temper and Plumb made edged tools for a lot of different companies and hardware distributors including Keene Kutter, Bluegrass, Simmonds, Marshall Wells, Montgomery Ward, Sears Roebuck, and many many more. If you know what to look for, you can tell who made the rebranded tools. The only tempering I would worry about would be really old edged tools or old blacksmith made tools. Also, years ago the threat of fire was a bigger concern than it is now. Any old tool that shows signs of having gone through a fire, pass it by (if you want to use it) because the tempering will be shot, unless you want the hassle of retempering it.
I still have my old Collins axe from when I heated with wood and it is an excellent axe. I also have some other True Tempers, Kelly and Bluegrass that are nice axes, and an oodles of various hatchets. I have a boat anchor single bit polled axe from Lowes that I use for logging. For most folks (including me), the making fine furniture usually doesn't involve an axe or hatchet, but maybe I'm just too nit-picky. I sometimes make sawmill slab benches and such, and use hatchets on those. I always sharpen axes with a file, never grind them, they are after all a fine edged tool. Last item- good wooden handles for axes, hatchets, hammers, etc are getting hard to find because there's only one wooden handle plant left in business I think.