Tiled is very frustrating at first glance because nothing is explained to you, even though the learning curve is not as high as it seems.
When you create the tileset, make sure to set it to "collection of images" and from the "Add Tiles" menu you should be able to select the entire "unsorted" folder, using the settings explained in the post above. I know I used to have problems when all of the tiles were a single image file, but as individual images they're already set to work.
Next you'll create a new map with the settings I've posted below. The red boxes are for the map dimensions, which will vary based on your project. Also make sure Stagger Axis is set to X rather than Y.
Once you do that, all of the tiles should line up with the map and show in their entirety. Then you can start exploring with layers for stacked tiles or adding structures and animal tiles, etc.
