What I generally recommend for mass market apps is to code for the latest or near-latest API level, depending on features that are useful in new API levels, and to simultaneously or soon after back-port a version using the compatibility libraries for older devices. Note that you can target higher API levels than phones in the the current sweet-spot have by testing for API availability (I.e. use forward compatibility, not just back-compatibility). Depending on the shape of the market, this can be a better alternative for some Android versions than using the compatibility libraries.
This puts future development on two, or, for very mature products, on three tracks where you have a code-base for up-to-date devices, and another for somewhat training edge devices, and maybe a third for old devices. Very often new phones have an outsize value to app developers because that's where the new phone customers, who buy apps at a higher rate than people with two-year-old phones.
YMMV. If you don't have tens of thousands of users, you aren't going to do it that way. Or, if you app has no need for the latest features, you won't do it that way.
This puts future development on two, or, for very mature products, on three tracks where you have a code-base for up-to-date devices, and another for somewhat training edge devices, and maybe a third for old devices. Very often new phones have an outsize value to app developers because that's where the new phone customers, who buy apps at a higher rate than people with two-year-old phones.
YMMV. If you don't have tens of thousands of users, you aren't going to do it that way. Or, if you app has no need for the latest features, you won't do it that way.