What are the common criteria of evaluation for a Post-Doctoral or Tenure-Track faculty position?
You seem to be most interested in a primarily research position so I'll say a few things about that and then give a broader answer. 

Every candidate is different, with a different mix of positive and maybe negative factors. Every hiring committee is different with its own concerns. Every university is different, and usually they have a well-defined "mission." 

But it is up to the candidate to make the case to the specific committee. Nothing positive that you do professionally is likely to hurt you unless your interests are wildly different from the "mission." So, for a research focused position at a university with a research focused mission all of the things you mention are good and any of them can be stressed in your application. 

All universities love that sweet sweet grant money and some fundamentally depend on it, so be aware of that in seeking employment. It is hard to get tenure in some places without quite a lot of grant support. Other places it means little, but is still valued. Especially if the grant can support students. 

However, you should try to match your own interests with the mission of the place. If you are very hot to do research you will be very frustrated at a place with little research synergy. Likewise there might be little future for a person interested primarily in teaching and advising at an R1 university. 

Note that some small Liberal Arts colleges have a strong research reputation, others do not. In the US, some state universities stress a teaching mission over research. Others are just the opposite. 

At one Ivy League college/university that I know of, faculty in Computer Science were (and maybe still are) given a choice of focus - teaching or research. They valued both and didn't require that every faculty be equally invested in both. But you had to excel in the one you focused on and be "acceptable" in the other. You couldn't ignore one aspect entirely. So, just as you need to make your own case for getting hired, you need to make your own case for tenure and the value of the various things isn't fixed in stone. 

Note also that some R1 level universities in the US have a special category for teaching faculty. The criteria for hiring and retention are quite different from that of the research faculty. There can be a place for both.

If you want to do research today, but are at a small place that doesn't support it well, you will need to establish and maintain a wider group of contacts, possibly world-wide. This was impossible before the internet and relatively cheap travel, but is now a possibility. In my later years I collaborated with an international group, a few of whom I only met face to face a few times. But it takes extra effort if the coffee-room crowd can't help you explore your current interests. 



Technical note. In some fields, such as CS, conference papers are extremely valuable. In other fields, not so much. Much of the intellectual life of the field can be carried on in good conferences.