IMO, 3k miles isn't much mileage on a 9sp chain...let alone cassette. Your chain broke, for whatever reason, and I'm not arguing against its replacement. But the cassette should last through the lifespans of multiple chains. I think there's a great chance you're rushing to replace your cassette much too early.
Get the 9sp chain you prefer, be it Shimano, SRAM or KMC. As you progress up the ladder, you get different finish/plating and possibly slightly lighter construction. You can use a connecting link with a Shimano chain, but it must be purchased separately.