Does anyone have any recommendations on health screening for specific cancers?

What specific cancers are you looking at? and what extras are you talking about?

The point of a screening test is to detect a disease that is common enough that it will make the screening worth the while. It should also detect disease at an early stage, for which something can still be done to treat the disease. The test needs tobe simple and highly sensitive to pick up the disease as well. Lastly, the disease progression / initial occurrence must be measurable, otherwise how you screen also cannot see.

Put all this together and what this means is that the "extra stuff" isn't really extra stuff. Health screenings are designed to screen these "extra" stuff because these are the ones that were identified at an epidemiological level to (1) cause most problems or (2) be easiest to treat and also (3) easy to identify with simple test.

Example: colon cancer? Big problem, affects many men. Can treat easily? Yes mostly, especially if picked up early. But prostate cancer? Also common problem, affects many men too. But serious? Not really, people tend to die WITH prostate cancer rather than die OF it. So screen? No point, because you dont change the outcome significantly.