The lighter, the better for performance. Barefoot wouldn't work as good, because shoes can have spikes or a tread pattern for better traction. The exception would be running in sand.
For training, you want a sturdier shoe that offers some cushioning from the shock. Training in a racing shoe will cause you some injury problems if you're putting in a lot of miles. If you have to choose between a better shoe for racing and a better shoe for training, go with the better shoe for training. The performance difference between running injury free and running with nagging injuries far outweighs any performance difference due to weight.
In high school, I had three pairs of shoes. A pair of racing spikes, a pair of training spikes, and a pair of training road shoes. I didn't run enough road races to make the expense of a fourth pair of shoes worth it. The racing spikes never needed replacing. I needed new training shoes about once a year, but we put in a lot of miles (70 to 100 miles a week).
For prolonged activities in the water, your feet will last longer in a good training shoe than in a racing shoe or barefoot. Plus, the bouyancy of a running shoe will cause your feet to float after they've detached from the rest of your body. Eventually, they might wash up on shore, providing your loved ones a body part to cherish.
A little like a message in a bottle proclaiming, "I'm dead! Stop looking for me!"
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