My ears were burning!
There are a couple of considerations in welding equipment.
First off, I wouldn't recommend gas welding equipment, although the techniques of oxy-acetylene welding are extremely valuable to learn. I would recommend arc welding for the garage hobbiest, right from the start. However, I would also recommend taking a welding class... and if you do, you'll learn gas welding first.
The central issue in welding metal together is that molten metal is very prone to destructive oxidation (rusting) while it's transitioning from liquid back to solid. It needs to be shielded. When you use an oxy-acetylene torch, the burnt gas makes a carbon dioxide environment around the weld and it actually prohibits reactive oxygen from reaching the metal while it's vulnerable. With arc welding, however, the heat source is from a high energy electric arc and there's no inherent sheilding effects. The metal oxidizes readily. It needs to be shielded by other means.
"Stick" welding (properly referred to as SMAW or Shielded Metal Arc Welding) uses a rod of welding metal that's coated in a powder layer that acts like a ceramic glaze. In the heat of the arc, the powder melts and drips onto the weld along with the metal, it forms a pool of molten glaze that floats on top of the metal till the metal is solid. This glaze prohibits oxygen from reaching the metal until it cools. Afterward, it's called "slag" and needs to be chipped off. Chipping and wire brushing these welds can be a chore, and the slag can become a problem. Incomplete cleaning interferes with paint. It also fails to get out of the way of new weld metal. If you weld back and forth, you'll create slag inclusions in the weld which significantly weakens the result. Good stick welds are as good as it gets. Bad stick welds are as bad as it gets, too.
One advantage of stick welding is that the shielding holds up well in the wind. This is an ideal situation for working outdoors in exposed areas like assembling a fence or a steel building structure. It's also a great option for an onboard system for trail repairs!
Wire feed welders don't suffer from the problem that stick welders do, in that stick welders require that you use a long stick that gets shorter and shorter till it needs to be replaced. The techniques of stick movement at the beginning are a bit different than they are at the end. Wire feed welders have a gun through which welding wire is delivered to the the tip and is electrified in order to create an arc. The gun allows the welder to have the same movement of the hands create the same character of weld all the time.
Wire feed welders can have "inner shield" or "flux core" wire ("flux core" is a misnomer - flux is a material that helps solder two dissimilar metals together so that they stick, while SHIELDING is for protecting weld metal from air) or they can use a shielding gas. Inner shield wire is still the SMAW process. There is a slag coating that needs to be chipped off of the weld at the end.
However, when a shielding GAS is used to protect the weld, the process is called GMAW or Gas Metal Arc Welding, and is also called MIG welding, or Metal Inert Gas welding. MIG is extremely convenient because the welds are clean as soon as they're cooled. They require just a bit of brushing to be re-weldable or paintable.
Wire feed welders of either the inner shield type or MIG are very practical for home use. Inner shield is slightly more economical because there is no need to get and refill a tank of shielding gas. One just has to buy wire.
Welding machines are rated by AMPERAGE and by DUTY CYCLE. A small machine that is about the size of a microwave can be run off of standard wall current (110 V AC, and a 15 or 20 amp circuit) and can operate for about 1 or 2 minutes out of every 10, meaning that it has about a 10 to 20% duty cycle. Many welding machines that are used to where they exceed their duty cycle shut off automatically.
10 and 20% duty cycle machines are very useful even though it doesn't sound like much. Welding for a continuous minute is a lot of welding! For most objects made from thin tubular material including round or square tube, flat bar, angle iron and plate metal are welded in short segments at a time. It would be common to weld a couple of inches on one corner, then a couple of inches on another corner, etc.
Most of the time spent on fabricating things out of steel involves shaping the parts that will be welded together and then preparing the metal for the weld.
The amperage capability of a welding machine roughly translates to be it's capability to heat into a piece of metal and get the mixture of molten metal from the parts and from the welding wire to deeply intermix and bond. If the metal can wick away the heat faster than the puddle of molten metal can form, then the weld will be "poorly penetrated" and weak.
For an entry level machine that can be used to learn and experiment, I recommend getting a small inner shield wire feed welder. Many of these can be up-converted to MIG with the addition of a tank of shielding gas and a regulator kit. These welders are capable of constructing many things out of thin structural steel. Thicker materials can be welded with multiple pass welds.
I took 3 semesters of welding and machine shop classes when I was in trade school. I actually trained as a commercial diver before I went back to college. I only started welding at home some years later, but the fact that journeyman welders looked over my shoulder and critiqued my technique was a huge leg-up on advancing my later capabilities. Formal instruction is SUPER helpful. If you don't go for that, at least get people who have done it for a while to work with you as you get yourself started.