I think your first step should be to find out what kind of wood it is. While hardwoods are generally good, soft woods, like pine are not much good. They burn quickly and explosively, and will gum up your chimney.
Assuming you have good wood, measure the length of the "rounds" and your fireplace or stove. You don't want to end up with 22 inch wood and a 20 inch capacity fireplace.
Next, consider your capabilities. We are a lot more sedentary now than we used to be, and I would guess that far fewer of us have the strength and talent to split wood with an axe (I looked at the picture of your axe and it has been around for many years with many names, and almost certainly you will have instances where you will get it jammed in the wood, so have something ready to get it out). It would be quicker and easier to just rent a splitter.
I started swinging a sledge at age 12, making gravel out of a concrete driveway with a 12 pound sledge. I hated it, but eventually I developed some skill and strength, so when hockey season came around, all of a sudden I had a great wrist shot. I should have thanked my father for that experience. After that, I split a lot of wood with the sledge and wedges. Sometimes I tried an axe, but always went back to the sledge and wedges. Today, having put on a few years, I would rent a splitter. My point would be that people, when I was young, had a lot of experience doing that type of work before they were even adults; I doubt that's true today.
I usually put the "round" > This is the very first time I am cutting rounds (cylindrical sections of