The peeler I have been using for the last 75 years is the square shape with the floating blade on one side of the square. You hold the other side of the square and steady your hand by holding onto the bar down the middle of the square. I pull the peeler toward me but you could push it away also. They are called "Wonder Peeler" and were made with a blue steel small curved knife or hook at one corner to dig out eyes. They stopped making the blue steel hook in about 1951, but I have found them over the years at thrift stores, rummage sales and auctions. I have at least 5 of them in my drawers now. The wonder peelers you can buy now have just an extension of the aluminum at one corner, but that is not sharp enough. If I had that I would switch to a knife to take out eyes.
Cooking potatoes with the peel is the best way. I cut the potato into large chunks so that everything in the pot is about the same size. After they are cooked, the skin does not "slide" off. You have to grab hold of a corner of peel (usually some of the corners curl up) and pull it off. OR - - you can eat that peel with the potato. Soooo good for you!