The best type of appeal to support the claim is an ethical appeal, which emphasizes the importance of pursuing meaningful work that aligns with one's values.
The type of appeal that best supports the claim that the best society is one in which satisfied people are doing work that matters is an ethical appeal, also known as an appeal to values.
In this case, Mill's claim emphasizes the importance of pursuing higher pleasures and meaningful work, rather than settling for basic satisfaction. This argument appeals to the values of personal fulfillment, self-actualization, and the belief that individuals should strive for more than mere contentment.
By highlighting the benefits of engaging in meaningful work that aligns with one's values and makes a difference, this appeal aims to convince individuals that a society where people have the opportunity to pursue fulfilling work is ultimately better for everyone involved.