Edisonck, the tire you need should be based on your tractor, it's weight, and how you will use the tractor a large percentage of the time.
I have tractors of various sizes, used for various task, and have R1, R4 and Turf on different machines. Turf tires are designed for, as the name mentions, using on turf. If your higher percentage of use is mowing on ground you want looking smooth, use turf. That also means you pay attention to soil conditions when you mow, but most don't mow the yard when wet. But then "yards" should not be worked on with any tread when they are wet.
R1 are the best for farming, working the soil. Obviously, that's what was first introduced in rubber farm tires. Hard to beat when you need the weight and HP of the tractor to move when working soil.
R4 is as heave industrial tread, ideal for many situations, but does not make ruts when R1's will. They are wider then R1's and heavier. Do not pick up nails and hardware on jobsites like other tires. Works find on yards when soil conditions are not wet.
Being in Mn. you need to evaluate snow removal. I've used R1 and R4 for snow removal and it does not make any difference to me. We get a few 6" events and sometimes to 15" max though.
Another nuance, I recently cut grooves in R4's. I can tell it makes a difference. But you're buying new tires, so you need to determine your primary usage. No tire is perfect for every application on one tractor.
I have an L4240 with R4's and 350# of fluid in each rear tire, and use it on my lawn for raking and other tasks. They do not kill, stifle or affect the K31 in my yard.
We use a Grasshopper Zero Turn for mowing, and the yard is Pretty!