O/A. The first welder we got was a blueshield duo light industrial torch kit from air liquide. I have nothing but good to say about it, all we did was add a smiths aircraft torch from ebay for the thin stuff. Just for the torch kit and tanks, not including the aircraft torch, was around $1000 (and that was after a big discount) I recall that the torch kit had a normal price of around $500, but he gave us a really good deal, so it cost around what the lincoln cutwelder costs ar home depot. He also gave us a really good deal on the tanks. If you want to get a good O/A torch kit that will last a lifetime, it will cost between $1000- $1500 (depending on how nice the guy at the lws is, and how good of a mood he is in) Now this seems like alot, but it is by far the most useful welder you can have. You can cut with it, gouge with it, heat with it, weld with it, braze with it, solder with it, even bend glass tubes to make neon signs. (I would like to see you do all that with a mig welder) Now in second place, I would put a good stick welder, they can weld thicker easier, but that is about it. I know you can use a carbon arc torch for heating and such, but it is not nearly as good as a big rosebud on an O/A torch. You can also cut with a stick welder, but the cut looks like it was done with a welding tip. Last in usefulness I would put a mig welder, just because it is basicaly only for welding thiner material. You can not do anything but welding with a mig. Sure you can weld thick stuff with a big mig, but it will be harder then with a stick. Also, mig is the easiest to learn, but the hardest to master, anyone can make a weld with a mig welder in seconds of training, but it will almost always be a poor weld. It is very easy to make cold laps with a mig, where as it is actually fairly hard to do with a stick welder. Look at the tests shield arc did with differnt stick electrodes, and also a mig welder. The mig is stronger, but if anyone can do that with a mig welder within a few days, I would be amazed. It is very easy to make mig beads look that good, but very hard to make them that strong. Where as with the stick welder, it would be much easier to get welds that strong.
Now for people saying O/A is only good for thin metal, and stick is only good for thick, I beg to differ. I have welder 1/4 inch wall pipe to 1/4 inch plate with my O/A torch, and it is very strong, 100% penatration. I have also welded 1/16 inch wall tube onto 1/4 inch angle iron with a lincoln tombstone with 3/32 rods, at 75 amps, and it worked fine, virtualy no burn through. (and I am not a very good welder, you could get as good as I am in a week or 2). I would say O/A first, but you can do well with either stick or O/A, as I said, I have done work I should have done with stick, with O/A, and work I should have done with O/A, with stick.