Hi. Great question. Overall, it depends on your problem how you assign cost to errors.
Precision is how many true positives of all your predicted positive
Recall is how many true positives from all actual positives
From this article
Recall is more important where Overlooked Cases (False Negatives) are more costly than False Alarms (False Positive). The focus in these problems is finding the positive cases.
Precision is more important where False Alarms (False Positives) are more costly than Overlooked Cases (False Negatives). The focus in these problems is in weeding out the negative cases.
Now, check this picture:
In that case, for precision false positive are more costly, for instance telling a patient that has a disease when it doesn’t have the disease
For recall, false negative are more costly, telling a patient that do not have a disease when he actually does have the disease.
Which one to pick it depends on many factors, on the pandemic, for instance, it was better to tell a healthy patient that have COVID-19 (False positive) than saying it was healthy since the treatment for many cases was to be at home, but the cost for telling someone that is healthy without being healthy (False negative) was greater at that time.
Let me know if this helps.