As a handyman, I have hung hundreds of very heavy items on walls. Sometimes I’ll use fasteners you would get at the store, and other times I use a French cleat. The French cleat is actually very simple. You can use whatever dimension of lumber is appropriate for the piece you are hanging, but you cut it at an angle along its cross-section. A table saw is perfect for this as you can tilt the blade and cut the angle.
You can cut the angle at 45-degrees on the table saw, and what you will be left with is a 45-degree cut on both pieces of wood. You can cut the length of the cleat first and then cut it on the table saw to make it more manageable.
You can hang a variety of things this way, from cabinets to shelves to fireplace mantles. You can use lag bolts into the wall studs for heavier items. The thing to remember is that with the cleat that is mounted to the wall, the lowest end of the cut gets mounted to the wall, and the highest end of the cut is furthest from the wall. This produces downward angle that supports the weight. The opposite is true for the object you are hanging. When you set the object on the wall, the top cleat rests on the cleat affixed to the wall and the angles of the mating cleats support the weight.