Anyone with a tractor and equipment should have a welding machine and heating apparatus of some sort. Things always bend and break and it is not practical to take everything to a shop to fix (that is my opinion). I have taught many classes in welding at both OJT(On Job Training) and college level course and they all start with stick welding, then after proficient at that, we start teaching TIG. In some ways TIG is much easier since it is a slower process and is usually more forgiving of a mistake. MIG is the last thing to teach even though it seems the easiest at first try. MIG is so fast that a beginner can put down enough bad weld in 30 seconds that would take 10 minutes to grind out.
Stick welding is probably the easiest to learn. You only need to control arc length and travel speed once the correct amperage is set. Lots of folks think MIG is easiest but there are so many things that can go wrong with MIG that will be catastrophic to the strength of the weld.
With a little bit of hands on instruction like you might get at a local college, basic stick welding can be learned in 2-3 weeks of practicing 2 hours per night x 3 nights per week if you have the natural ability. However, some students never make a good welder even with a thousand hours of practice. This is why I suggest that you enroll in a welding class to get the basics learned (if you a naturally inclined) prior to purchasing a machine. You will then determine which process better suits your needs. Then you will just need practice to get better.
For my farm needs, I only have a nice AC/DC stick machine and an oxy-acetylene torch (both bought used) and with those I can fix anything that breaks or bends. I could add a TIG torch and a bottle of argon if I needed to weld a bunch of light gauge stuff, but so far in 10 years of having my "farm", I havent needed to use TIG.