Random selection is the key to ensuring that the members of a Federal Council are independent, diverse, and protected from any outside influence. Each applicant would have an equal chance of being selected from the pool.
There may be some minimum required qualifications to serve on Federal Councils, similar to taking any federal civil service position. In addition, some Federal Councils may have specific qualifications in education or experience. Testing would ensure a necessary understanding of the concepts rather than a specific college degree or job title. Some councils may require a background check or even a security clearance. The government would pay for testing, background checks, and security clearances when needed.
Certified curriculums could be created by colleges and even high schools in some cases to prepare applicants to qualify for Federal Councils who would otherwise find it difficult to meet the requirements. Scholarships or free online training could be provided as needed to ensure every group had an equal opportunity to apply to a pool.