To sum up: it's up to you to choose what an interesting effect size is.

There are several measures of effect size, not just the variant of Cramér's V you mention. Here is a non-exhaustive list*:

1. Cohen's w,
2. Fei coefficient,
3. Pearson contingency coefficient

(see the effectsize R library for more information about these last two).

These coefficients can be converted between them, and in particular to Cohen's w. Cohen's w is often used for power/sample size calculation (e.g. see the pwr library in R).

You may stumble on some websites mentioning some general guidelines for the interpretation of Cohen's w or Cramér's V. These guidelines generally come from Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed)  (see this question for more information about that).

  But what is an interesting effect size is ultimately up to you, there are no universal guidelines that apply to any situation. As Cohen says in his book (p.224):

The best guide here, as always, is the development of some sense of magnitude ad hoc, for a particular problem or a particular field.

In other words, the question you have to ask yourself is, for example: does it matter in any way, if some cells deviate of 1% from their expected values? Would the following table be interesting for your research question?

Each of these tables has a different effect size. Read about previous research on your ongoing subject of study, think about what kind of tables would be little interesting, somehow interesting, very interesting, with a difference between cells so large that it would be completely unexpected, or with a difference so small that it would not matter the least.

Preferably, you should do these calculations before running your study, as sample size calculations require you to pre-specify the smallest effect size you're interested in. Maybe add some safety margin to your initial calculations to avoid ending up with an underpowered study.

*NB: Unless I completely misinterpreted it, researchers in genomics seem to use different measures of effect size for power/sample size calculation than those I mention above (see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4133582/ for example), probably because they deal with complex categories that come in millions or billions. But that's not my field at all, so I can't say much about that, and I may be a bit off the mark.

What is an interesting effect size is ultimately up to your judgement, there are no universal guidelines that apply to any situation. Some guidelines taken from Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed) are sometimes followed (see this question for some details about Cramér's V and Cohen's w). But as Cohen says in his book (p.224):

The best guide here, as always, is the development of some sense of magnitude ad hoc, for a particular problem or a particular field. Since it is a function of proportions, the investigator should generally be able to express the size of the effect he wishes to be able to detect by writing a set of alternate-hypothetical proportions [...], and, with the null-hypothetical proportions, compute w. Some experimentation along these lines should provide one with a "feel" for w.

In other words, the question you have to ask yourself is, for example: does it matter in any way, if some cells deviate of 1% from their expected values? 5%? 10%? How many cells should be affected by a deviation for the table to be interesting? For example, would the following table be interesting relatively to your research question?

And so on. 

Read about previous research on your ongoing subject of study, and think about what kind of tables would be borderline uninteresting, somehow interesting, or very interesting.

Preferably, you should do all these calculations before running your study, as sample size calculations require you to pre-specify the smallest effect size you're interested in. Maybe add some safety margin to your initial calculations to avoid ending up with an underpowered study.