Big Serrated Rib
Small Serrated Rib
Serrated ribs are great for score-and-slip, and for making textures in the surface of pieces. If you plan on attaching more than 6 handles in your lifetime, you won't regret picking this up.

Fettling Knife
A dull paring knife from your kitchen is OK, too. Remember, knives with removable blades are not allowed in the studio.

Teeny Kemper carving tools
These are my favorite little wooden fingers for reaching into small spaces and moving clay around attachments. Also a good upgrade for sgraffito.

Clean Up Tool
I was skeptical of these for a while, but now I use them alongside the small wooden tools. Sometimes a curved metal blade is just the right thing. Available in a few different sizes and combinations.

Sharp Steel Trim Tools
These are good carving and trimming tools for fine lines and details, including sgraffito. Maybe not great for work-horse, everyday trimming. Speaking of which, trimming tools do wear out and need to be sharpened or replaced from time to time.

Really good lookin sgraffito tools by Zebra
Some of you have asked for better sgraffito tools - the needle tool isn't the right tool for much of anything! I've never used these, but they look like the Cadillac for carving lines!

Really affordable sgraffito tools
I've recommended this to a lot of folks, also great for signatures.

Bear Claw
Scoring tool for scratch-and-attach, or texture. The needles are a bit further apart and heavy-duty than a serrated rib.

Ball Point Stylus
A more expensive cousin of the "dull pencil." I use this for mishima (inlay) work and it comes in different sizes so you can make thick or thin lines. Also good for signatures.

Bamboo Barrel Brush
This is the fluffy type of bamboo brush I prefer for putting down thick/solid/consistent layers of decorative slip. Available in different widths and you can break the barrels apart to split it into multiple brushes.

Hake Brush
Real similar to the barrel brush, just not what I use.

Bamboo Lettering Brush
Fluffy bristles hold glaze and wash really well, and it comes to a point. I like something like this for line work. I think I probably have a XXL and a Medium or Large in my studio.

Stiff Brush
I have something like this around for brushing the crumbs out of scraffito lines. Keep the brush dry, and keep it clean so it doesn't spread too much dust.

Lid Calipers
Some sort of calipers are necessary for lids. This is sort of a deluxe set, simpler is OK too.

Fancy Cut Off Wire
If you're interested in upgrading your cutting wire, check out a few options - different types of handles, different thickness of wire, and different lengths. I use a 7" thin wire from Dirty Girls most of the time.

Soft Rib
You're probably going to come across these, this is my favorite flavor. I have a soft rib to help smooth attachments. Mud Tools Ribs are available in different hardnesses. Sometimes a longer, firm rib is helpful for plates or bigger stuff.

Rounded Wooden Rib
I like this rib for plates and also bowls. The wooden rib that comes with the kit has that pointed end that sometimes gets in my way, so I have a rounded one. Check out the other shapes and sizes too, sometimes a different shape is useful for different things!

Finishing Sponge
Something like this can also be good for smoothing texture around an attachment or edge--it has a finer texture than the yellow throwing sponge. TBH I use white triangle make-up sponges instead.

Diamond Sanding Pads
If you're interested in a smoothy-smooth surface, hit your work with a sanding pad after the final firing. There are great because you can use them wet to prevent dust from spreading - always polish your work wet! Be careful, these do scratch glaze. They last forever. I have a 60 grit and a 120 floating around my studio. 3M also makes some pads that are nice, too.

Artists Masking Tape
The jury's out a little on this one; I don't use a lot of tape. This is useful for masking good, straight, hard lines primarily on bisque ware. I recommend something a little stretchy and not too papery. Some tapes come in a variety of widths so you can have different size lines.

PS - take this chance to get a notebook or app to keep tabs on your work, too!