What to do if your phd went well? I will soon be in my final PhD year and am about to start my job search. Suppose that for some reason I suspect that I did quite well, research-wise. My main question is:


  What is the optimal job search strategy/advice in this case?


Generally, I can think of two options that are "better" than a regular postdoc:


A fancy fellowship or a named postdoc position
A tenure-track (TT) position


First, do I have to decide between postdoc and tenure track before getting an actual offer? That is, is there anything special I need to do when applying for tenure track besides pressing buttons on mathjobs.org? (Also, is there an option I missed?)

Second, I have questions about each option.

Option 1: Is there a comprehensive list of "really good" postdoc fellowships? Or can we combine a list here? I know that there is Clay fellowship, Miller fellowship at Berkeley, Society fellowship at Harvard, Veblen instructorship at IAS. What other well-known similar positions come to your mind? How do they compare between each other, and to a regular postdoc or a tenure track?

Option 2: Since this depends on many random factors, it seems like if I apply two times, that is, apply next year and then (if I only get a postdoc) apply after my postdoc ends, the probability of landing a nice TT job increases. On the other hand, the quality of a TT job offer I can get after a postdoc will likely be higher because I will have better publications. So I'm not sure whether it is even worth it to seek a TT position now as opposed to settle for a postdoc right now and just apply for TT in 3 years after it ends. Although I've seen people switch between TT jobs, I don't know how common that is. Also, how much of a blocking factor here will be not having lots of teaching experience? (I have some but not as much as most postdocs.) Finally, I understand that when applying for postdoc, I should prefer schools where my area is represented best, but this seems not too crucial when applying for TT, right?

--

To be specific, the field is pure math, the country is US, and I am not eligible for NSF.

A couple of other disclaimers: I understand that the answer depends on my priorities, so let's say the top priority is landing the "best" possible tenured position I can at some point in the next ~7-10 years (which includes not having to teach too much before getting a TT job offer; money is not too important to me personally at this point). I also understand that it's very hard to tell objectively how good my research is, but for the sake of argument let's assume that it's good enough, comparable to other TT job applicants.
You’re overthinking things (but not by much, and in a way that is both typical and understandable given your current situation and vantage point on the job market for academic math positions). 

The main things you need to know are:


You don’t need to make any decisions until you get an offer.
You don’t need to do anything “special” when applying for jobs other than follow the application instructions, and there isn’t much else you can do to gain an advantage, other than obvious things (like proving a major result, winning a major award, and having strong visibility in giving talks at various places, especially departments where you’ll be applying).
Your chances of getting a tenure track offer straight of your PhD at a very good (say, top 50 R1) US university are pretty low, assuming you are an average person who meets your description of yourself in the question.
Your chances of getting a tenure track offer at one of the top math departments in the country (like the one you mentioned in the comments) straight out of your PhD are extraordinarily low, again assuming you are an average person who meets your description of yourself, and even assuming you are quite a bit above average. Of course, there is a possibility that you are a person for whom this is a realistic prospect, but if so then I would say you have been rather modest in your description of yourself.


The bottom line is that at the moment your optimal strategy is the obvious one, which is to apply to any place/position where you think you have a realistic chance of getting an offer (and if it doesn’t embarrass you too much, even places where you don’t think you have a realistic chance). Once you get some offers, you may or may not be faced with a minor dilemma of the kind you seem to be worried about. But there’s a good chance that won’t happen (e.g., you’ll get a few postdoc offers and it will be fairly obvious which one is best for you). And even if it does, I think it will become fairly clear in due course what is the right choice. Trying to preemptively make strategic decisions of the kinds you are thinking about long before those decisions are even applicable and when you don’t have all the information is pretty much a waste of your time and mental energy.

Good luck!