How many times you handle wood is a lot dependant on where the wood is coming from and how much equipment, you have to handle it, as well as how much room you have to do the processing. Picking a large firewood tree up out in the woods carrying it on your shoulder to put on your truck or trailer isnt a real option unless you either have equipment, or you cut the tree into manageable sizes first. If you have to cut the tree into round sizes before you can load it, its obvious, you are going to have to make several trips from the stump to the truck before its all loaded. And if its a good sized tree, its also a sure thing those big pieces are going to be a lot easier to carry if you split them first. You have to split them regardless if you do it in the woods or you do it right beside your wood pile, the difference is in how any trips between the stump and the truck you have to make. Then you also have the chore of unloading the wood from the truck and stacking in the rick, or under the shed, on the pallet or what ever.
Now if I can add one piece of equipment to the equation, it would be some way to eliminate either some of the carrying of rounds, or some of the loading and unloading. If your getting your wood miles fro home, you either have to haul in a piece of equipment to do the carrying and loading with, or you got to do it all by hand. For one tree, I would just as soon process the tree where it falls rather than have to trailer in another piece of equipment. If the tree is close to the house, I'm going to use whatever equipment I own. The wood I have been getting across the field from my house we started out just bucking it into rounds and throwing on the truck. Just a few little pecker poles, no big deal. Then they wanted to take out a few bigger trees, and they where over a steep bank. I wasnt about to carry the wood up that bank and thru the brush, so we took the tractor and pulled the trees out of the woods. Well the first couple of little trees, we just bucked and threw on the back of the truck, no big deal. Then they decided to cut a few more trees, well, we had to skid them out and they where already hooked to the tractor, and my house was just a few hundred yards away, so we just skidded the trees right up beside the wood pile. Doing so meant a lot less handleing of the wood. Saw it down and trim it where it lay, drag the whole tree right to where I would be splitting it, no loading and unloading, no stumbling thru brush, and no heavy lifting.
Now if this wood had been farther away than just across the field, and equipment was already on site, I would have taken my dump trailer and loaded the trees in log lengths and dumped beside the wood pile to be processed later.
Bottom line is I dont think there is a one size fits all approach to gathering firewood, and once it is gathered, there are just as many ways to process it as there are people doing it and the brands of saws they are using.