I'm not that familiar with oxy-acetylene welding (only did it a few times), but I can offer some response to the arc welding methods:
SMAW (aka "stick" welding): Easy to change different filler materials (electrodes) but some are difficult to learn without training (for example - welding nickel based alloys on cast iron). This process is better for welding thicker metals together (over 1/8") and has the lowest initial setup cost.
GMAW (aka "Mig" welding): Used frequently for welding sheet metal with a wide variety of filler metals (wire) and shielding available. Unfortunately, you need to match the filler wire and shielding gas type by switching spools and tanks. Considering the maintenance items (tips, liners, wire feed rolls) it's comparatively expensive to run compared to SMAW (above).
GTAW (aka "Tig" welding): Like SMAW, changing filler materials is easy. You might also need to change shielding gas (and use a diffuser for carbon steel processes), depending on the application. This is one of the most versatile arc welding processes and can be used on very thin materials. Since the filler and torch are usually held in separate hands, it's a bit more of an "art form" to produce really good welds. This is the most expensive of the three processes, and requires maintenance items like tungsten electrodes, collets, diffusers, and gas cups. There are also items like high frequency start pedals/switches and water coolers that can be added to increase precision and longevity of the torch.
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I'm currently using an old Lincoln "225 amp red barn" AC (stick) machine. It has definite limitations - especially on thin materials. But, I've built a lot of work tables, brackets, jigs, and other tools with it.
I'd love to get one of the new "Tig" inverter type machines, but that's still pretty far down on my list of "Gotta Haves".
