Raspberries are my favorite, but I like all of those berries and they are great in their season. We have an abundance of strawberry plants in the garden, and there's nothing quite like eating them fresh picked. We also live in an area that produces blueberries, so there's a time in summer where they are everywhere, and people eat them by the handful at picnics and cook-outs.
For picking, I'd definitely pick blueberries. The bushes are the perfect size so you don't have to bend over, like strawberries, and there are no thorns to navigate.
The area I live in does not, however, have a lot of blackberries. I used to live in the Pacific Northwest, long ago, and blackberries there are roadside weeds. People are constantly fighting down blackberry brambles threatening to take over fences. You can get all the free, beautiful, big blackberries you want at the height of the season.