Your best approach would be to speak with your veterinarian to determine which tests are appropriate for your bird.
However, I can help you to rule out some of the listed tests, because they are not necessary for birds. Newcastle Disease, Infectious Bronchitis and Avian Influenza are diseases that can be present in birds. Feline Leukemia and Feline Panleukemia are common diseases for cats. Canine Parvo Virus is a disease that primarily impacts dogs. Brucella Abortus, FMD (foot and mouth disease), Strangles, Babesia, Thieleria, and Trypanosoma are diseases in horses or other livestock. So of the first thirteen tests, you really only need to consider three. Newcastle Disease and Avian Influenza are listed twice - looks like they have two different ways to assay these diseases. Ask your vet which one is more appropriate for your bird.
The tests listed under "blood chemistry" might be useful as a baseline for the future and to identify possible health problems. RFT and LFT probably stand for "renal function test" and "liver function test". These tests will check if your bird's kidneys and liver are working. T3 and T4 are thyroid hormones. You could check this, just to see if it is normal. Abnormal results would indicate a problem with the thyroid. Serum Electrolyte is another good one. If anything is out of whack it could be an early sign of health problems.
The tests listed under "other clinical tests" include CBC (complete blood count) which looks at the number of blood cells, like red blood cells and white blood cells. This can be a useful diagnostic test, since abnormal cell counts can be sign of disease, like anemia or leukemia. The fecal parasite and blood protozoan examination are both looking for signs of parasites in poop or blood, respectively. For the fecal test, you would need to provide a fresh sample of waste. Before asking for this test, be sure to check that they are able to test samples from birds. This is a pretty common test for dogs/cats. Culture Sensitivity is a test that is done on a sample to determine antibiotic resistance when bacteria are present. You generally would not perform this test unless the animal is suffering from a known infection.
So if you eliminate the tests that are not related to birds or don't make sense to attempt on a healthy bird, you are left with this list:
Newcastle Disease
Infectious Bronchitis
Avian Influenza
Serum Electrolyte
RFT
LFT
T3/T4
CBC
Blood Protozoan Exam
Fecal Parasite Exam
Of these tests, I think the blood work (CBC, Serum Electrolyte, RFT/LFT, thyroid tests) are probably the most useful. They will provide information on your bird's current health and serve as a baseline, if your bird gets sick in the future. You can ask your vet about also doing the fecal parasite and blood protozoan examinations to check for the presence of parasites, if they feel that is necessary. I would also ask your vet if it is worthwhile to test for Newcastle Disease, Infectious Bronchitis, and Avian Influenza. Since your bird is asymptomatic, I think these test are more likely to come back negative, however it might be possible for your bird to have the disease and only present minor symptoms.
