What to Carry: Mining
-Pickaxe of your choice
-2 Spare Pickaxes that are stone or iron
-Food, preferably a stack or half a stack of steak/cooked porkchop
-A stack of Cobblestone
-Sword of your choice

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What to Carry: Exploring
-A Stack of cooked food or bread
-A Sword
-A spare pickaxe (in case you find a mine)
-Some blocks to make beacons if you find an interesting area
-Map (Optional)
-Knowledge of your house's coordinates

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What to Carry: PvP Combat
-A Sword, iron or diamond, optionally enchanted
-A bow with a stack of arrows (or one if enchanted with Infinity)
-Potions of Swiftness, Strength, or Health
-Good knowledge on PvP combat
-Food if you lose hunger during said battle

I'll add more as I think of them into Part 2. It is presumed that you wear iron or diamond armor in all of the 3 events stated above. Like and diamond, it really helps me out, and I will be posting another soon! See you all later!

My Engin Wall: www.supercraftbrothers.com/profile/2589140#post8612520