For ranking the carbocations in the image above, I thought of taking the approach that the 1st molecule, the secondary carbocation was the most reactive because it has no electron donating group, then the carbocation with a terminal NH2 because nitrogen has an electron donating group, then the tertiary carbocation, and lastly the last carbocation has resonance making it very stable and less reactive. Is this the correct train of thought?
Order of stability: 3 > 2 > 1 > 4
I would say that the third structure is the most stable (least reactive) as an octet-complete resonance structure of it exists which is much more stable that the initial carbocation. This is basically what you said, the carbocation is stabilized due to the electron donation tendency of the nitrogen atom in this case.
Then structure 2 then 1 since 2 is tertiary while 1 is secondary. More the alkyl groups, more the positive inductive effect stabilizing the carbocation.
I would say that the fourth structure is the least stable. If you try to draw the resonance structure in which oxygen ends up donating electrons stabilizing the carbocation, you'll notice that the oxygen ends up with a positive charge which is even more unstable than the initial carbocation. Resonance does not help here.
(the structure above should have a positive charge on the oxygen; I wasn't able to draw that using the software available)
Do note that resonance structures don't actually exist and there are better ways to explain more or less the same thing. I've stuck with resonance since you've mentioned that in the question.