You would want a PCR swab test only if you had a lesion to swab. It is NOT to be used in asymptomatic people and it is NOT to be used as a blood test. The PCR test is looking for virus itself, not antibody, and virus is not normally found in the blood of adults.
Yes, the test they are describing is the one you want. Do NOT get an IgM test – this is useless and confusing.