The core values of an agency foretell the kind of relationship you will have. Generally, consider agencies that are collaborative, innovative, and proactive.  The best agencies really stand out when transparency and accountability are also baked into their corporate culture.
By asking questions about their corporate culture, this should also give some insight into an agency’s hiring process. Since the greatest benefit of partnering with an agency is its team, getting a measure of the agency’s talent is essential. Also, be sure to check out what employees say about working at the agency on sites like Glassdoor.