I believe there is a regular rotation when pruning Blackberrys, Gooseberrys and Raspberrys.
If my memory serves me correctly, you should be pruning out the oldest Canes, probably the 5th yr or older Canes. Fertilizing in the early Spring and early Fall, not over Winter in my area. Up to a Half Pound 5-10-5, spread around the entire root system of the Mature Plant.
First year Canes normally do not produce fruit with the rest of the plant, only 2nd, 3rd and 4th yr canes, older Canes also run out of Gas or Die off.
Cuttings taken from either 2nd or 3rd yr Canes usually have no problem rooting. And the tip of any Cane that bends over and touches the ground will root into a new plant.
WARNING ! You can easily get over run with Blackberrys, Gooseberrys or Raspberrys if the tips of the Canes touch the ground.