I've never quite understood why their shields don't offer any resistance until they adapt and become immune.
As I said earlier, it's mainly because not all drones HAVE shields. Different drones have different sensor/tools/equipment fittings that are optimized for different situations, and not all of them are "hazardous environment" types.
The Borg adapt by changing their equipment to fit the situation, once they determine what the situation is. If you kill their first drone, they'll send one you can't kill. If you kill him too, they'll send another one even harder to kill. Same appears to be true of their ship: if their main weapon can't affect you or if you demonstrate the ability to defend against it, they'll toggle to a different weapon that's more likely to be effective.
The Borg possess such a broad arsenal of equipment that all they have to do is figure out which of their drones/gadgets/tactics will work on their adversary of the day. Their singular advantage is that they can do this instantly, by sharing information among themselves and immediately figuring out what parts they need, who has them, and where to use them.