Here I'll list and describe my favorite supplies for math and science related tasks. I'm fairly particular when it comes to tools; my father -an engineer by trade- always liked to say that I should seek out the "right tool for the right job." This statement seems more obvious for engineering disciplines, where the tools are often machines of various sizes; however, I have found it to be equally important in mathematics and theoretical physics! The pencil, paper, chalk, board, software, etc. can be a source of friction for me if chosen improperly, perhaps you feel the same. If so, the below selection of products that I use regularly might be useful to you!
Likely the most frequently used tools for students, the pencil is important. It needs a good weight, decent grip, and the ability to deliver crisp lines. I find sharpening pencils tedious, so the only pencils I use are mechanical. I favor the rOtring due to its heavier weight, but also use the Kurutoga occasionally - its automatic lead-rotation mechanism keeps the equations sharp even when I have to write small. The last item here is a gateway-pen, the Parker Jotter. I call it a gateway pen because it was the first fountain pen I used, after which I never used another type of pen again. Fountain pens can get quite pricey, so this one is a good, cheap, entry-level option, perfect for every-day use.
Gotta have somewhere nice to take those pencils and pens for a drive! Good quality paper helps to preserve your notes while making the tactile nature of writing easier and more enjoyable. Paper is especially important if you are using a fountain pen, as they ink will have a tendency to seep into the paper (Moleskine is a bad paper for this).
The Leuchtturm notebooks are perfect notetakers, coming with labels to help you organize and a table of contents that you can fill out while you go. Some might suggest that this product is similar to Moleskine - you're not wrong, but you're not right. Moleskine uses much cheaper paper, and doesn't (at the time of this writing) have a dot-pattern paper, which is great for physics and math when we like to juxtapose words, diagrams, and equations. The Rhodia pad is ideal for homework since it is easy to tear out, but high enough quality to want to keep post-grading. The Ampad is a good cheap lab notebook or scratch pad.
Ah, chalk. My favorite tool. We could have an entire discussion about "why do you use chalk?" I'll briefly say that chalk, while possessing all the tactile delight you could desire, also offers practical advantages over dry-erase markers. Specifically, chalk doesn't need to dry when you erase, so it doesn't slow you down. It never stains the board, isn't harmful to smell, doesn't dry out, is much cheaper than markers, on and on I could go... To those that complain about the dust, use microfiber cloths to erase - it will greatly reduce the amount of dust (conventional erasers just smear it around).
Of all chalk makers, Hagoromo is my favorite (and I think this is a common opinion in the math world). The story behind the company and it's relationship with the math community is long and interesting, you can read more about it in this excellent Gizmodo piece. Fortunately for us, this story ends with the chalk being available on Amazon! I use the white chalk for nearly all writing, occasionally using the red and blue colors for diagrams.
When it comes to chalk erasers, there are three fundamental choices: felt, sponge, or cloth. I personally prefer the form factor of the felt eraser, though find that the microfiber cloths work the best at removing chalk. They are also easiest to maintain, since you can just throw them in the washer!
Some useful-but-optional chalk accessories. The chalk holders are nice if you like to keep your hands a little cleaner, or have a hard time gripping the smaller chalk pieces. The chalk case is useful when traveling.
Give a nerd some chalk, he's going to want a board. The BestRite boards have been around (and American made if that's important to you) since the early 1930s, and have been the university standard since the mid 50's. These are a little trickier to buy, since you'll need to contact a dealer; if you have the patience to go that route it is worth it! If you have a hard time finding a dealer, feel free to email me and I can put you in contact with the representative that helped me buy a couple. If you want the simpler solution, the Quartet boards on Amazon are nice too. Make sure to stick with the porcelain board if possible, they make for better surfaces than the synthetics.
This section is under the "if you want to treat yourself" condition, in that most of these suggestions are on the expensive side of the spectrum. However, I've gotten an immense amount of utility and mileage from the below items, and use them regularly.
Hope you enjoy these tools as much as I do! If you have any additional suggestions feel free to leave a comment.