Hi PJ-
Yes, "buzz box" is a slang term for an arc welder. These do not require gas because the weld is shielded by the flux coating on the welding rods. Advantages of arc welder:
1) As I mentioned, they are relatively cheap
2) Unlike gas-shielded welders, they can be used outdoors in the wind (wind disturbs the gas shield and messes up the weld).
3) Can lay down a darn-nice looking weld. IMO, a nice arc weld bead looks better than a MIG weld bead - you can get that nice, shiny "stack of dimes" look with an arc welder.
Disadvantages of arc:
1) The flux coating forms a glass-like slag on the weld that protects it as it cools. Generally, you'll want to knock off all the slag. Certainly so if you intend to paint. This takes time, and if you want a clean shop floor, needs to be swept up.
2) Welding rods are consumed and need to be replaced often. So this takes a little time also.
3) Require a little more practice on "out of position" (vertical or overhead) welds. But if I can learn to do it, anybody can!
IMO, the main advantages of MIG over arc are that out of position welds are easier, and also the "trigger" on a MIG welder is nice - there's no chance of accidentally giving yourself "arc eye" as you can with an arc welder by accidentally touching the arc rod to the base metal before you intended to. Buying an auto-darkening helmet will make this a non-issue (they're great!). And since MIG doesn't require you to change welding rods or pound slag, you can get more welding done every hour - a good thing for a pro that welds for a living, but not too big a deal for a hobby welder.
The cheapest MIG welders frequently cannot run gas and instead must use flux-wire. Welding with flux wire produces slag on the weld like arc welding, but they can be used in the wind. Any welder that can run gas can also be used without gas by running flux core wire.
FWIW, I've never found keeping gas bottles around to be a problem. Even though I'm only a part time hobby welder, I've been at it long enough to know that it's something I'll keep at for a long time, so I went ahead and bought bottles (oxygen, acetylene, and CO2). I bought half-sized bottles that are easier to handle but still big enough to not need replacement very often at all.
The inspection on the tanks is good, I think, for five years. But that's not an issue for me. The welding supply shop where I bought my tanks takes care of that for me. I bring in an empty bottle and then pick up a full bottle that has been inspected. If I wanted, they'd let me leave my bottle and then pick it up a day or two later and always keep my original brand new bottle, but it's much more convenient for me to just continue to swap them out in one visit. Since I bought my bottles, all I pay for is the gas I use, and there's no monthly charge - all the advantages of bottle renting, but only a single up front charge.
You are right about being able to lay down multiple passes with a small welder. The smaller welders, however, will not get the penetration into the base metal that a larger unit can. So, for instance, if you're going to "butt weld" to pieces of 1/4" flat steel to each other, you can use a small welder and lay down a few passes along the seam, but the weld will mostly just sit on top of the metal and not penetrate into the core of the two pieces being joined.
You can work around this a little by tapering the ends of the two pieces of steel so that when they are butted together, there is a little valley between them that you then fill up with weld in multiple passes. This would be fine to do now and then, but I'd not want to have to do that often as it would take a fair amount of time.
IMO, in addition to the lack of penetration with small welders, an equally significant problem with them is duty cycle. This is the amount of time that they can spend working versus "resting". This resting time is critical to allow the machine to cool. The higher you crank the output voltage/amperage of a welder, the lower the duty cycle will be. In some cases, the duty cycle can drop to a horribly low 10% or so, so you need to make sure and spend LOTS of time allowing the machine to cool, or risk burning it up.
If a small welder is advertised to be able to weld "up to" a certain thickness of steel, that maximum thickness is guaranteed to be at the highest output setting and as a result will have the lowest possible duty cycle for the machine. If, however, you buy a machine that's advertised to weld steel that's quite a bit thicker than you think that you'll want to work with, this tells you that for the work you'll be doing, the machine will be set below it's maximum output setting and the duty cycle (higher to begin with on larger machines) will be increased even more.
I guess everything's a compromise. Some welders have advantages over others, but depending on how much use you plan to put a welder to, it's possible to work with what ya got and just live with the shortcomings. I do think that a cheap 220V AC arc welder gives the most power and highest duty cycle for the money. As was mentioned, with 3/32 welding rod, you can weld some fairly thin stuff. I use arc to weld 14ga steel with no problem regularly. Anything much thinner and I risk burning a hole in it. The main thing I like about the 220V arc is that it's plenty big to weld trailers, hitches and other "heavy" things at about half of it's maximum output. And since you'll have to stop now and then to change rods, etc, the duty cycle will never be an issue with a machine that size.
I'm sure that Harv has waaaaay more experience than I do. I'm really no expert. I guess my main motivation in posting is to encourage others to jump in and give welding a try. With no formal training and some reasonalby cheap equipment, anybody can be making some pretty neat stuff with just a little practice!
Best,
Mark