Express Entry: Use the CRS Calculator to calculate how many points you will score, assuming highest IELTS score and spouse’s MSc (say YES for ECA). Then check the recent cutoffs to see if you will clear it. If you do, now would be a great time to apply. If not, you may need job experience and/or PhD to clear the score. I applied under this category. Your lack of foreign job experience/Canadian job experience might a negative factor in scoring enough points I think. Try simulating scores for
- both you and your wife together, swap for primary applicants,
- Individually (i.e. selecting spouse as “not accompanying”),
and see which combination scores better and whether it clears the cutoff.
CEC (Canadian experience class): If you get Canadian work experience you can apply under this category. I do not know much about this category.
PNP (Provincial Nomination Program): Once you study and/or work in a province that province can nominate you and it’s pretty easy getting PR through this. Since you are headed to Montreal, Quebec has it’s own nomination (QSW Quebec Skilled Worker) or Quebec Experience Program where you need the Quebec selection certificate to qualify. Quebec is kind of a country in it’s own right, with it’s own immigration stream separate from the federal skilled worker (FSW) or PNP. I do not know too much about PNP, QSW, QEP either, but I do know that once you are nominated by a provice and receive PR, you are expected to live in the province for a period of time before moving out, with some exceptions.
As you can see, once you’re in Canada, you open a lot more doors than applying from outside. Also, you may be able to work with a student visa and apply for PR before getting PhD.
P.S.: Is your future research in deep learning?