We have torch, MIG, TIG, and stick welders in the shop, I've used them all for various different tasks, and I teach welding to a few students a year.
MIG has a short learning curve for most students, once the settings on the machine are set correctly, it's just a matter of keeping the gun the right distance from the work and putting the weld in the right place.
Lincoln and Miller both have good small units that will plug into a regular 120 volt 15 or 20 amp outlet. Don't sweat a 20% duty cycle. Unless you set up a factory in the garage, the actual time spent welding pales in comparison to the time spent clamping, jigging, grinding, cleaning...We have a few of those units that are in regular use in the shop and that we take out into the field. The only one we ever burned up was a Hobart Handler. The Lincoln units sold at the "big box stores" have different model #s and the welding stores will tell you they are not as well made, but having been inside machines from both sources, it's the same parts inside...One difference to be aware of is whether or not the gas solenoid for MIG welding and a regulator is included. It frequently is not on the "big box" welders, and both are fairly expensive items to purchase. If you want to MIG instead of just fluxcore weld, you'll need both and they are usually included with the welding store models, which makes their prices look more reasonable. For welding steel, use C02 if you are cheap, or an Argon blend. The initial cost of an Argon blend is high, but a bottle of gas lasts a long time if you are not using it every day. If you want to weld aluminium too, get a welder that you can attach a "spool gun" to and a bottle of pure argon gas.
An Oxy-Acetylene torch set is very versatile, you can weld almost any metal that will melt (assuming you have the right flux), cut steel, braze, solder, etc. For most of my students, it also has the longest learning curve. There are a lot of variables to get just right, how far from the weld to hold the torch, how fast to travel, how much filler metal...and they are all directly controlled by the welder.
TIG is much like an electric version of torch welding, and once you master torch it's not hard to learn TIG. Miller has a couple very nice little inverter based TIG units that can run from a 120 volt 15 or 20 amp outlet, and can weld up 1/8" material with that input, unfortunately they are expensive. TIG can also be used to braze and can weld any melt-able metal, even titanium if you have an inert gas filled enclosure. Most TIG power supplies can also be used for stick welding. With TIG you can weld steel or aluminium using the same bottle of Argon.
Stick welding has a medium learning curve, and the common AC "buzz box" welders can sometimes be had pretty cheaply at garage sales. They are power hungry, (30-50 amps at 220 volts) but if you have an electric dryer or range, they can be wired to plug into that outlet. Stick welding material thinner than 16 ga. is not easy. Stick welding really shines for thick sections. DC stick power supplies can be used for TIG on steel with the proper equipment
Which one should you get? If you are only going to join steel, then MIG. If you want more versatility, Oxy-Acetylene or an inverter based TIG unit.
