The last time we went through this process, 5-6 applications seemed like enough. My S knew just what kind of college he wanted. Many schools that interested him were within a day’s drive; the others were similar enough that we thought we could delay visits until after decisions rolled in. So we didn’t need to pile on more applications just to compensate for uncertainty about what he wanted. If you’re less sure about what you want, if you’re counting on competitive scholarships (or on need-based aid with estimates all over the map), if all the schools you like are too far away to visit conveniently, etc., then you may need as many as 10 (or even more) applications.
In my opinion, there is no such thing as a “second tier” medical school, but virtually all of them are very expensive (with little/no aid available other than loans), unless you get your medical training from the US military. So for many families, net cost is an important (maybe paramount) factor in choosing a college. For many upper middle class students who are serious about med school, the choice to beat is your state flagship. If your family income is below $60K or so, a very selective private school may offer a lower net cost. However, you don’t have to attend an Ivy to get into a “good” med school, nor should you need to attend a low-ranked school in a distant state just to get an adequate GPA. Try to identify schools with affordable net prices, then from those, use your judgement to find the best combination of quality and personal fit.