Basic welding equipment?

I’ve had some broken tools I have wanted to repair for a while. This spring that includes the shovel! So I have been thinking—look for someone who welds? Or maybe find some equipment to weld them myself? I do have some cursory arc welding experience, but that was years ago.

Do you have any recommendations as to basic welding equipment?

Need more hints.  What do you want to weld?  Heavy metal work?, lighter metal work?, Aluminum?, cast iron, hydraulic lines?, thin carbon steels?.  Do you have 3 phase?, 220?, 110?, DC batteries.

I have a broken shovel and scythe blade to fix, but also a cast iron cauldron with a crack.

I don’t know the latter terminology, but we have ordinary electric AC power (connected to grid).

Sounds like a low-cost 110 volt wire feed welder would do most light jobs.
Very easy to learn how to use, small, lightweight, and portable.  
Cast iron welding is not for a novice. Special welding rod and proper heating and cooling are needed.
Here is an example.
https://www.harborfreight.com/easy-flux-125-amp-welder-57861.html

MIG (wire fed) welder is the most user friendly, but at the same time it can not be purchased too cheaply, because it has mechanical parts and cheap mechanical parts will fail and jam. Welding high carbon steel and cast iron is not easy nor pleasant, so it may be a turn-off.

I do a lot of welding, it while it is easy to do, its not easy to do well.
Unless you plan to build things and learn about the functions of welders I suggest you get some one to do it for you.
Enrolling at a welding school is a great idea, that is how I learned, 55 years ago.

If you are looking for a good farm welder, a mig welder is a good place to start.  It is easy to operate and the learning curve is shallow.  Just know its limits.  in the hands of a good welder it can weld almost anything a stick welder can weld.  In a home/farm setting, most of the repairs one will do are within its capabilities (1/4 inch material or less.)  They are not so expensive anymore.  The more you pay the more reliable they become, but an inexpensive one will do most of what you want.

An import stick welder can be had very inexpensively.  They are a bit more 'touchy' to pick up the skill, but do the job for light repair.  Home repair welding can be fun, but like other 'hobby' can get costly.  If you only have a few repairs, it may be cheaper to pay someone whom has the equipment, skill and knowledge to do it right the first time (especially the cast iron.)  That said, I think more homesteaders and self reliant types should acquire some skill with a welder.  Start with mig.   Learn what good penetration looks like.  Have some fun and enjoy the new skill.

you can weld cast iron with nickel rod, stick welding , when you get a welder there are all kinds of inexpensive inverter welders available these days, look for one that is a AC/DC multiprocess, so you have stick, mig, tig options. lots of good videos on YouTube for lessons

Do all welders need a specific diameter of stick or wire?

There is abundant barbed wire fencing that I have unwound that I might be able to use.

M.

What makes a welding rod work in stick welding is the coating or flux on the rod.  As the metal burns away under current, the flux burns and creates A bubble that excludes oxygen from the puddle and reduces oxidation in the weld, which weakens the weld.  With Mig the wire is either protected by an inert gas or a flux filler inside the wire.  

Rods come in all different lengths, diameters, and coatings.  The barbed wire will melt, but will not make a suitable weld due to voids and contaminants in the finished weld.  

That makes sense. I know I read about that yesterday but forgot this morning.

Oh My, the short answer is YES, welders require the proper size stick, or the correct size wire.
What you are thinking of is called gas welding; no welder is required, but it uses a torch to melt metal.

One more caution for anyone reading.  Barbed wire is often coated or galvanized.  This contains zinc.  Welding on zinc coated material (or with coated wire) produces a nasty gas you don't want to breathe.  Use a respirator under your welding hood.  If not you will get sick for a day or so.  Welders call it "zinc flu" because it comes with flu like symptoms for a day or so.  bad juju.  Be safe.

This barbed wire is really old and needs to be de-rusted, likely no zinc left. But I suppose I should take slow reliable steps and not dive into anything crazy at first!