How should I store a broccoli crown?

Keep it dry and refrigerated, loosely wrapped or in a perforated bag, and use it within about four to five days. Moisture speeds yellowing, so don't wash it until you cook it.

Yes. Peel the tough outer layer and slice the stalk into coins or matchsticks. It takes slightly longer to cook than the florets, so start it first.

How do I keep it from going mushy?

Cook briefly and hot: roast at high heat, steam for a few minutes, or stir-fry. Boiling for a long time is what turns it soft and dull green.

Is it better than frozen broccoli?

Fresh has firmer texture and more bite when roasted or stir-fried. Frozen is picked and frozen quickly and works well in soups and purées, so the better pick depends on the dish.