What benefits would Americans with Greek ancestry get if they apply for citizenship in Greece?

An applicant whose ancestor was a Greek citizen can approach the Greek Embassy or the Directorate of Civic Status of the Decentralized Administration of the area where they reside with the following documents:
• Registry of the ancestor in Greek municipal records.
• Documents that prove relationship to the Greek ancestor.
The estimated time for this process is 18 months.
On the other hand, the process for the 5-year long Golden Visa, residence-by-Investment program, is done through the Consular power of attorney within two-to-three months. The Golden Visa permit also entitles one for citizenship-by-naturalization applications.

If you have Greek roots, it is easier to get citizenship. If not then you need at least seven years of legal residence in Greece.