You'll get mixed answers on this. Many prefer chains on the turf tires over chains on lug tires. Chains on lug tires tend to allow the chains to fall down in between the lugs/treads, not providing as much grip. When the chains are on the turf tires, all of the chains protrude past the tire tread, giving the most traction.
One trick that many overlook is to use narrower tires with chains for snow plowing, then wider tires for summer use. The narrower tires with chains will give you less tire surface area touching the ground, which provides more pounds per square inch (PSI) on the ground, giving you a better bite in the snow/ice, and better traction. The wider tires will work better in the summer, giving more surface area touching the ground, which provides less PSI on the ground (less traction), and leaving fewer tire tracks in the yard.
As for front tires, many to use the lug tires to help with steering. I personally have never thought that this was much of an issue, and always just used the ribbed tires like came on the CC tractors when new. There is really not much you can do if your are pushing on ice, as the weight of the snow typically pushes the front of the tractor around quite a bit. If you are using a snow blower, you can usually lift the snow blower slightly, to give more down pressure on the tires, and better steering.
Bill
