As a professional recruiter, here is my take.
1) I usually have work for welders, and pipefitters, but usually have enough resumes coming in that I don't spend much time advertising on them.
2) I rarely have needs for Millwrights or Mechanics as I see far less turnover for these trades, when I do hire for them I find that they can be harder to find than welders, or pipefitters.
3) Most places I have consulted for have ongoing needs for electricians, and I can spend literally thousands advertising for them and not see a single resume for months.
Going in I would consider looking at the millwright, or electrician path as they seem to offer the highest demand/greatest stability. If I was going to choose welding I would make sure to do it in Alberta and go the distance to receive my B-pressure ticket. Personally I would stay away from Pipefitting as it has become more specialized, (bench fitters, sprinkler fitters, ect) I do not have a high demand for this and you can be certain there are many other fitters who have experience doing it.
my 2 cents