I am a new member and don't even have an airframe at this point, but what I do have is 3+ decades holding a welding torch of one kind or another. My experience spans from fillet brazing 4130 steel tube bicycle frames, tig welding the same frames, tig welding aluminum bicycle frames and tig welding titanium bicycle frames, and tig and mig welding 304 stainless steel sheet and tube. I can tell you with assurance that gas welding the airframe is fine. Do what most of the people recommended, which is namely practicing a lot on stuff that doesn't bear a lot of load before you go onto the critical airframe. Once you feel like you've got the hang of it, do the critical stuff.
The first step to any good weld is a really good fit up of the joints. Think of the welds as just glue made of similar material. What you want the welds to do is transmit the stresses going through the airframe without becoming a riser for them. If the tube fit up is good (as in about .005"-020" gap) all around when you make your tacks you've got the basis for a good joint. Sloppier joints are more easier dealt with using a gas welding process as you can fill it in with the rod material a bit easier.
A good way to think about the weld strength is to apply the weakest link notion. The joints concentrate the highest stress loads, everyone will agree with that. If your welds are less strong than the tubes they connect and the loads on the joint come up to the point of yield of the tubes, then your joint is going to fail at the welds. So how strong should the welds be? Well, that E70-S2 weld wire someone mentioned earlier has about 2/3 the tensile and yield strengths of 4130, so whatever the tube thickness is you should be about twice as thick with your weld bead. Once you’re able to complete a uniform weld (remember, a thin or gapped portion of weld bead will be the stress riser) that’s about twice as thick as the tube you’re down the road.
Notice I didn’t mention gas or tig on that last paragraph? That’s because either is just fine, both will work, but in both cases you need to observe the size of the weld bead. Full penetration, twice as thick.
Do you need to anneal or stress relieve the welds? Gas welding: No. The time it takes for a skilled welder to create that weld will almost be twice as long as with a tig welding process. The tube soaks up this heat and it travels down the tube, expanding the heat-affected zone by a notable margin. Remember that the load stress is concentrated at the joint. A joint with a relatively large heat affected area has a longer transition between full strength tube and softer annealed tube. This long transition virtually eliminates the stress riser. With tig welding, at least in the hands of a skilled welder, the total heat the joint absorbs is far less, and the heat affected area is also far less, and therefore the transition between full strength tube and a softer annealed tube is much more abrupt. IE, a stress riser. In this case some stress relieving torch application is a really good idea.
My comments on mig are this: Yes, it surely can be done. But you need to know what you’re doing. You need full penetration of the weld. It’s easy to create a nice looking mig weld that doesn’t penetrate to the root. That is a weak weld. With practice, yes, you can surely do all the joints with mig process. But practice is the key. And like tig, you’d probably want to stress relieve it afterwards.
We never used mig process on bicycles simply because the welds were too large. Too large meant too heavy. Bicycles are models of weight paring. Grams count. That’s why fillet brazing virtually disappeared: Too heavy. But it made a great joint. Everything annealed nicely as with gas welding, and with full penetration and a root thickness of 2-3 times the steel it created a fail proof joint.
And as others commented: Never quench a weld, and no, you don’t need to pre-heat the joints for any of the weld processes being considered here. The tubes absorb the heat quickly and you don’t lock in the stresses as you would with thicker material that takes longer to heat.
So if I were you, and I was a novice, I’d definitely gas weld it. It’s hard to deny the success of many thousands of airframes built this way. If you were a skilled tig welder, use that method. Then stress relieve the critical joint areas that see lots of load. If you mig lots of tubing all day long and knew the process well, then by all means do that. And stress relieve it as above. If you were chasing the grams, then tig process is without question the way to go. With excellent tube fit up in the joints you can create a uniform weld that in the end will be the lightest of all, and as strong as necessary. But at the end of the day, done well none of these process are going to lead to a bad outcome.
Final note: I’m well aware I’m leaving some stuff out here (like the relatively minor but notable differences in joint strength between tig and gas welded joints, and the finer points of stress relieving a joint), but even if I included it all the advice I gave would be the same. The points others made about the cost of a decent tig machine vs an oxy/acetylene rig (easily found used on the craigslist or at your local flea market) are completely valid also.
Good Luck!
Gary Gable