The only few soft general rules when it comes to minimum wages.
- The higher they get relative to median wage in the economy the higher the probability the utility cost of minimum wages imposed by higher prices for consumers and higher unemployment outweigh the benefits.
This is already what the source you found said:
The main finding is that the positive effects prevail when the starting level of increase in the minimum wage is very low and the economy is in a negative output gap.
The more elastic demand for labor is (e.g. this typically occurs when labor can be substituted for by use of capital etc.) the more negative effects minimum wage will have on employment (e.g. see discussion in Borjas Labor Economics ch 3).
The more perfect the market is the more negative effect minimum wage will have. This is because minimum wage can be shown to have virtually no negative effect if there is monopoly or monopsony or just generally non-trivial market power of the producer on the market (either goods market or factor market). In that case market power may create quasi rents - a situation where firm gets some pure economic profit which provides larger than necessary reward for firm owners.
I think this point is best to illustrate with example. Suppose, we have some firm with market power (meaning it can sell its product above marginal costs). Suppose that the only source of cost of this company are wages and it currently pays wages \$20 and sells its product for \$40. Meaning it has net economic profit of \$20 (please don't confuse economic profit with accounting profit - economic profit is not the profit firm reports on profit and loss statement and pays taxes from). Now if there is \$20 economic profit, that means that the firm earns \$20 more than necessary for it to produce this product and supply it to market. This would be called quasi-rent (or Marshallian rent) please don't confuse it with prue economic ren't which would occur with windfall profits.
Now as explained previously firm will happily operate whether it get's this quasi-rent or not, so from societal perspective there is no reason to allocate this quasi-rent to the firm. If society implements minimum wage that raises wages from \$20 to \$40 in the example above, the firm would still supply the same amount of products and kept the same amount of employees. Although point 1 would kick in here at minimum wage that would push wages above \$40.
The more you care about minority groups the less you would want to increase minimum wages. Now this rule applies only to an extent you believe minorities should get special treatment to offset the fact that they are historically marginalized. If you do not care about this you can skip this point, but nowadays it is fashionable to care about diversity and inclusion, so I thought it might be relevant to mention it.
Research shows that minimum wage has much higher negative impact on marginalized groups (see Garry Becker, 1957; Williamsa 2011). This is because asking for lower wage than majority is a natural way how a minority can offset negative effect on their employment from stereotypes or racism etc.
The above being said these are all very soft general rules. It is much better to in each case empirically examine parameters of the market.
In fact, all of the above general rules need at least some (even though not necessary rigorous) empirical examination, since its hard to know how many substitutes there are for labor, or whether there are quasi-rents (you can't just say that because firms report profit there are quasi rents since firms report accounting profit not economic one etc).
In addition, the general rules above won't really allow you to put numbers on those effects. Just generally it can be said that typically if demand for labor is elastic the negative effects will be larger, but you can't know how much, which is always relevant. Lowering employment by 1%, while increasing wages by 5% and increasing prices by 6% is completely different scenario from lowering employment by 10% while increasing wages by 5% and increasing prices by 30%.
As a result, for anything else than just a pure back of the envelope calculation, it would be best to perform or commission an empirical analysis of the industry where you want to implement minimum wages, to see what are the expected effects of minimum wage on that particular industry. Probably post-implementation you would still want to do some re-evaluation because it is hard to model general equilibrium effects so you would want to double check your early estimates against actually observed effects.