Well, it was a ranch and not a farm, but I can tell you what the armament was on our place in west TX the 1940's-50's.
My dad's Remington Mod. 8 in.35 Rem.; my Remington Mod. 141 in .30 Rem.(our deer rifles); a Winchester Mod 69 bolt action .22 (given to me by my uncle before he died in WWII); My dad's Remington M11-48 12 ga.; my Mossberg bolt action 20 ga.; a Stevens single shot .410 pistol (that rode in a hand made holster on my dad's saddle for snakes); an H&R Mod. 922 .22; Later, I got the two Colt SAA's in .45 Colt and .38-40 handed down from both of my grandfathers. Except for during deer season, the old Winchester .22 rode in a rack in the pickup. As you can see, handguns were pretty scarce.
Since this is a farm instead of a ranch I agree that the protagonist will spend a lot more time on a tractor than a horse. The danger of getting some appendage (either one of his or one that he has hung on his belt) hung up in machinery is very real! Unless he will be actively dealing with large farm animals like horses and cattle that might injure him or themselves and cause him to have to shoot them, there is little need for a handgun. If I had to choose what I would carry on that tractor, it would be the H&R M922 .22 (pretty undramatic, what!)
Since it was long before the advent of radios or phones, one use that we always had in the back of our mind with our guns was for signaling back to the ranch house in case of emergency...three quick, evenly spaced shots would bring anyone in hearing distance running.
Bob
PS If you are going to be realistic, remember that firearms on a ranch/farm are just a tool. Don't attribute the romanticism that the movies have done. They are no more or less than a saddle, tractor, hammer, etc. and the proper tool for the job is the answer. Just decide what the job is for the handgun of your character.