The tools are self explanatory, Gravel and sand for getting in ravines or deep holes if there is no other way down, dirt and cobble in case I need to make myself a bridge, torches to light things up, and food for when I'm hungry.
This is for exploring and such. Any specific situation will just replace one or two items.
4. Building block or, in the rare event that I'm carrying one, hoe.
7. Misc (if I have a bow, I usually put it here)
8. Misc (if I have arrows, I usually put them here to keep track)
1. Diamond Pickaxe with Efficiency III, Unbreaking III & Fortune III
2. Diamond Sword with Sharpness IV
3. Bow with Power IV and Flame I
8. Food (currently cooked chicken) - I try to have at least 20
5, 6 & 7 may have different items depending on whether I'm exploring outdoors or a cave, or a mineshaft (a stack of cobblestones in one of the slots is useful for mineshafts), or building.
If I'm exploring outdoors, I'll keep about 10 dirt in slot 5 and a bed in slot 6. When it gets close to dark (about the time when the sun touches the horizon), I will set up the bed by making a 2 block high tower then sneaking out 2 blocks past it. I then put the bed on those two blocks.
4. Arrows (I keep them in hotbar so I can see how many I have left)
I never use any tools but pickaxes frequently. On a mac trackpad, 9 is an easy key to reach with right hand so I put torches there. 1,2,3 can be reached from WASD so I put weapons and blocks there. Finally, knowing how many arrows I have is a personal preference, has saved my life several times so I can see when to switch to sword (I play by only using skeleton dropped arrows, so I never have very many)