Here are the tools that I use for throwing (clockwise starting with the red calipers).
1.) Amaco's "Lid Master" Calipers- These are great because one side measures the opening of the pot and the other side measures the lid. I also use these when I'm making sets of bowls or cups to make sure the mouths are the same width.
2.) Wire Cutter- I use this to cut the pots off of their bats.
3.) Stainless Steel Trimming Tool- I bought this at NCECA and am having a hard time finding one like it online. I use this mostly for trimming tumblers.
4.) Small and Large Kemper Loop Tools- I use these for trimming everything else. I only use the small one for doing the insides of the foot for teacups and mugs.
5.) Yellow Sponge- I use this for soaking the water out of the bottom of pots, wetting the clay while I'm throwing, and cleaning off my wheel and tools. Sometimes, I hold it in my right hand when I'm making a pull. I usually only do this when I'm throwing something larger, like a jar or flower pot.
6.) Spatula- I use this for scooping the sludge out from the bottom of tumblers and other tall forms.
7.) Wooden Knife- I use this to undercut the clay before I cut it off the wheel.
8.) Needle Tool- I use this rarely...sometimes to cut the top off of a wobbly pot.
9.) Right Angle Rib- I use this for compressing and squaring the bottom of tumblers.
10). Flexible Metal Rib- This is my favorite tool, the one I use the most! I use it to to compress the outside of pots while I'm throwing and also while I'm shaping the pot. I love the subtle lines it makes and the smooth surface it creates! I also use it on bowls and saucers. It's great for making a crisp edge!
11). Rubber Rib-I use this when I am making bowls to compress the bottom and form the inside curve.
I also use Kentucky Mud Works' Universal Bat System. I don't have a lot of room in my studio, so storing pots on 5 1/2'' square bat inserts is a lot easier than storing them on 13'' bats. I used to use pot lifters, but didn't like the way they would warp my pots. I've been using this system for over a year and it works beautifully! Honestly, I don't take very good care of the inserts. I only clean them right before I use them and they are in great condition still!