October through April are the peak months for fresh broccoli. You always want to look for firm stalks with tightly bunched heads. Don't choose broccoli that heads show signs of buds turning yellow; those little green trees are over the hill. For storing, you can keep fresh broccoli in the fridge (in a plastic bag) up to 4 days.
For recipe ideas and nutrition information, see Superfood: Broccoli.