I have the bike upside down when I put the wheel on. I adjust the cone by the sprocket before putting it on. You should feel just a slight amount of side to side play in the axle. After tightening it on the bike, check the roll of the wheel. The chain can make a difference if it is too tight, leave some slack in it. if it rolls well, good, then check the bearings side to side play.
If it's got a lot of play, or is binding, I loosen the sprocket side, keeping the other axle nut tight, and use needle nose pliers to adjust the cone on the drive side. If there's room when you back off the nut, a wrench would be even better. I adjust about 1/4 turn at a time, then tighten it back up. Your wheel should only have a tiny bit of side to side play. Check it again because it may change as it's tightened. That should get you where you need to be.
If you have the hub lubed and adjusted perfectly, it should last for years.