Hardwoods are dense and difficult to chop quickly. They will provide a long and cleaner burning fire, though, which is better if you will be needing a fire for a long time. Examples of hardwoods are hickory, oak or maple.
Softwood burns quickly, which is good for a quick cooking fire while camping. Softwoods are usually easier to chop and split than hardwoods, and they dry out quicker so they can be used earlier. Some examples are pines, cedar and fir.
There are plenty of potential firewood chopping tools. Most people use a light maul, which can be swung fast and strong. Others use heavy mauls, or short axes and hatchets. Some people use a wedge, which is a piece of metal that can be hammered into a log slowly and carefully.
Start out with a wide stance. Measure your striking point by pointing the maul near the edge of the log, which is the best place to hit. Holding the maul with one hand at both ends, swing it strong over your head, slip the top hand down to the base of the shaft, and use force to bring the maul down on the wood. Never remove your eyes from the striking point.