Following Chrismahon's thoughts, I would add that a small - say 100amp rated AC welder (the output is an alternating current) - is a very useful basic welding set.
You can join steel up to about 1/4" thick reasonably well. You can add a carbon electrode to the welder to use it for brazing. This allows you to join thinner sheet steel by melting brass rods with a powder flux. This is something like super strong solder. Welding anything thinner than 1/8" thick is very tricky as the current will just melt away the steel before you can make a join unless you are very experienced. But you can make a brazed joint in thin steel quite easily this way and you do not need an oxy-acetylene or propane burner and gas bottles.
You can get special welding rods which you can use to rebuild worn parts. The weld metal is built up in layers on things like the tips of mole and ordinary ploughs, the teeth on back-hoe buckets, etc.
Now a basic welder set like this will probably require its own 30amp socket. This isn't difficult to get installed but a standard 13amp plug and socket won't cope.
If you want to go further into welding, you can get a DC (Direct Current) set. This lets you choose whether the welding torch is positive or negative. For a trained welder, this allows more control for different jobs.
You can also get many different types of welding rod for special jobs like welding upside down. I doubt this is of interest but it is nice to know there are options if you need to tackle something that is fixed - like the steel in a building or on a big vehicle.
MIG (Metal Inert Gas) and TIG (Tungsten Inert Gas) welding sets are used for more special sorts of welding. They are more expensive but you can do things like welding aluminium and stainless steel. Some of these sets use carbon dioxide when welding thin steel and some use an inert gas like argon. The latter is pretty expensive, CO2 is fairly cheap.
If you buy a basic welding set and find it tricky, don't be put off. It is easiest to start with a strip of something like angle iron held in a bench vice. Weld along a flat horizontal line to practice. Striking the arc by touching the tip of the welding rod on one of the strips sounds easy but the tip will stick until you get the trick of touching them and instantly lifting the rod to create a small gap in which the arc forms.
Once you have mastered this trick, practice creating a smooth regular line of weld by gently rotating the tip of the welding rod over the small pool of molten metal on the surface of the angle iron.
If you are right handed, point the tip of the welding rod at about 45 degrees to the left and create the line of weld steadily from the left end of the join. That way the weld can be seen from above through the mask.
Sorry if this is turning into a long story but there are a few little things worth mentioning.
NEVER look at the arc. This will give you arc eye. This normally comes later in the day and is like sunburn on the retina of the eye. It can be very painful and leave permanent damage. Keep children and animals away from the area at all times.
Be careful about the spray of molten metal that comes from the welding process. it will set fire to wood, straw paper etc. It will also burn you and make holes in your clothes!!
Keep a full bucket of cold water at your side. You can immediately cool any burnt part of your anatomy in it and put out small fires before they take over.
You should wear leather gauntlets and a leather or heavy canvas apron or overalls to protect yourself and your clothes when welding.
Some clamps are very useful to hold metal together temporarily while you weld them. The welding rod sticking to the metal will misalign any parts not securely clamped. It is often best to make small welds along a long join before trying to create a large structure. These are called tack welds. They stop the parts distorting as you weld. Otherwise you can start with straight pieces and finish up with something with a slight curve where the metal has expands as it is heated and then if fixed in that position by the weld as it cools.
You need to clean off the layer of slag formed from the coating on the weld rod before making another weld over the top or starting from a previous weld. Also clean off the slag before painting. This is done with a small hammer and a wire brush.
Sorry again if this sounds too much. But a little trial and error will get you welding and the benefits are significant if you have to make tools or repair them. You get a stock of old pieces of metal which you can convert into useful equipment with very little effort.
Good Luck