How do you set goals and manage priorities across a marketing team?

Show a system that connects company objectives to individual work.

• Start from the business target — revenue, pipeline, or growth — and work backwards to what marketing must deliver. Goals invented inside marketing that do not ladder up to a business outcome are how teams become irrelevant.
• Use a goal framework consistently. OKRs are common: a small number of objectives with measurable key results. The discipline is keeping the number small — a team with twelve priorities has none.
• Distinguish outcome goals from activity goals. "Publish 20 articles" is activity; "increase organic pipeline by 30%" is an outcome. Activity goals are easy to hit while achieving nothing.
• Make ownership unambiguous. One person accountable per goal, even when several contribute.
• Review on a regular cadence — weekly on progress, quarterly on the goals themselves — and be willing to kill work that is not moving the number.

On priorities: protect the team from constant reprioritisation. Absorbing every incoming request is what makes marketing teams busy and ineffective; saying no, or saying "yes, and here is what drops", is the manager's job.

Note: Mentioning that you leave deliberate capacity for the unplanned is realistic and credible — a fully committed team cannot respond to anything.