Your inventory for training can and should be fairly light. You will need food, but do a practice run with a full load and see how much you really need. If you can't get a couple hour run in with 10 lobsters, then only bring 10 lobsters. Your goal should be to keep your weight low to save energy. Have your run on! Only bring what you need to stay there for about an hour to three hours, and then take a break to bank. You might have to bank some random or drop items.
You might want to bring potions to help you hit higher. For the best results for your money, buy combat potions! These help out all of your stats, attack, strength, and defense, letting you hit higher more frequently while blocking more of the Rock Crabs hits!
In your inventory for pking, you could have the choice of going basic, or advanced. A more basic would be some food, maybe lobster, regular strength and attack potions, maybe combat potions, and a teleport tab.
A more advanced is like the picture shown below. You will have super sets, which is super strength, attack, and defense, monkfish, prayer pots, and a teleport tab. You really don't need to have super defense. It does not help much. However, supper attack and strength are highly recommended!!