I’m not a fan of the Priority custom field! Nine out of ten times I see it used by clients, I feel they’re wasting time and recommend they remove or replace it.
A Priority field is shown in many Asana demo videos and is included by default in many Asana-provided project templates. I feel most of these are not optimal.
Simpler Approaches
In cases where a task has a Due date set, a Priority custom field often is redundant; the Due date effectively conveys the priority, so a custom field is not needed.
I always first try to use the position of the task in the tasks list to convey priority by using grouping and/or order.
In My Tasks, I have sections including Now, Today, or This Week to group tasks by priority; no Priority custom field needed. In deadline-bound projects, sections indicate Phases or workback structure (Six Months Out, One Month Out, Week Of, Day Of) to group work. And in each of these cases, I maintain priority and/or chronological ordering within the sections instead of using a Priority custom field.
Benefits
I feel the above approach is simpler (better organization, less visual clutter) and more efficient (you don’t have to set the value of an extra custom field value for every single task). That last point is crucial: More often than not, when a Priority field is included, people forget or don’t bother to set these values for many tasks. What does that mean, then? That its priority is undefined for some reason? Or does it mean that it’s a Medium priority? Then why have Medium as a value too? And for that matter, how often do you see Low or Medium values used? In my experience, the most used values are High and not set.
Preferred Alternative
If you really do need to indicate importance beyond using the Simpler Approaches I suggest above, I recommend using a Critical or Hot custom field. Make it a single-select type but with a single option value: 
(checkmark emoji) or 
(fire emoji). (This is effectively creating a checkbox field depicted as a single-select type field because Asana doesn’t offer a checkbox appearance, but we can simulate it this way)
There’s no task-by-task overhead of setting a value (as there is for setting Medium) because the unset default is usually what you want (most tasks are not critical).
It stands out more than High because it appears in a column of otherwise mostly empty cells.
You don’t have to decide if it’s Medium or Low, often a meaningless distinction.
When to Correctly Use Priority
I hedged in this post’s title using the word “usually.” There are legitimate and valuable uses for a Priority custom field.
One example: If you do sprints and have a Backlog project, it’s helpful to have the backlog prioritized; High, Medium, and Low have strong meanings here.
You could do that with sections as mentioned in Simpler Approaches, but using a custom field might offer more flexibility (use of filters, rules, appearance elsewhere when multi-homing, etc.). And you could still sort (group) in List view by Priority to effectively turn the High, Medium, and Low values into what appear like project sections.
No Free Lunches
Priority is the only free custom field Asana makes available to the Asana Basic plan. Don’t use it just because it’s free!
I wish Asana would provide my Critical custom field above as a built-in custom field and also make it available in the Basic plan. and use it instead of Priority in demos and Asana-provided project templates.
Thanks for reading,
Larry
