I understand the USCG for example always use a rescue cage (may be wrong here) while UK helicopters will use a single strop, a double strop or one of a variety of stretchers as the case demands.
Not correct on this point, but the rest all sounds good. More or less similar to how the UK does it, though the "basket" as the USCG call it is a sentimental favorite due to various historical factors such as small cabins and a somewhat late arrival to the rescue swimmer/diver party.
As far as range, it will depend a lot on where on Spaceship Earth you're operating. The U.S. has areas that go offshore to only about 150nm and some areas if there's an appropriate unit with aerial refueling or that can island hop or lily pad (ship hop) that can go out several times that distance. The scope of your ship operations will essentially determine what available SAR assets are available throughout your area of operations.
While I can't speak for people worldwide, at least in the USCG case it is generally welcomed if you discuss these matters over a hot beverage on a pleasant day before things start going pear-shaped on a dark & stormy. Much like visiting ATC in their lair... they tend to be rather pleasant folk and not at all the ogres they can be on the radio.