What was the main concern of the Delian League?

Answer 1

Originally? To unite Greeks against the threat of the Persians.

After the defeat of the Persians? To execute and maintain Athenian hegemony in the Aegean.

Or to put the second point in another way, to give Athens the money to keep its fleet in place to enforce the annual collection of funds from the members, and spend the rest of the tribute on improving its own city and keep half its people on the public payroll.