Freshly picked blackberries make the most flavorful ice cream. Blackberries have a great texture, but its flavor is more subtle than the wow! factor that fresh blueberries give blueberry gelato or ice cream.
I went to Larriland Farms in Maryland and got over 20 pounds of peaches, blackberries, and freshly cut flowers. If you're in the DC area, it's a wonderful way to spend a weekend morning.
Blackberries are ripe and ready for picking when they are very purple-black and they easily come off the stem. Although the unripe red berries would be terrible to eat, I still think they are the prettiest.