Is there a standard set of genetics tests for a person who has 2-3 close family members with cancer?

Genetic counselling. You will need to have a genetic counselling. They will be able to tell you your risk for possible genetic abnormality/syndrome and what tests you would need to have. There is no a standard set of genetics tests -all will depend on your family history of cancer.
No single test. Even in persons with multiple family members with cancer, there is not a single genetic test that can pick up different cancers. There are specific tests for some cancers, e.g., colon cancer. Almost all genetic tests require expert consultation.