Calcium tartrate is a great high speed introduction to crystal growing because it is very forgiving and "magical." You can get ~millimeter size crystals in seconds. Then once you're hooked you can try growing crystals that require more patience/technique. If you ever saw the demonstration of lead (II) iodide precipitating from solution [1], this demonstration looks similar except that the crystals are sparkly and colorless instead of sparkly and golden.

You'll need potassium hydrogen tartrate (cream of tartar), sodium hydrogen carbonate (baking soda), and calcium chloride (sold as DampRid or Pickle Crisp).

Add a spoon full of baking soda and a spoon full of cream of tartar to a glass of distilled water. They should fizz together as the baking soda neutralizes the acidity of the cream of tartar, releasing CO2. This is what you want, since the mixed neutral salt of tartaric acid is more soluble in water. Stir and wait for the fizzing to die down, then gradually stir in small portions of more cream of tartar until the additions stop dissolving. Let the solids settle in the glass.

Meanwhile, dissolve a spoon full of calcium chloride in a second glass of water. It should dissolve readily with a bit of stirring.

Once residual solids have settled in glass one, decant the clear liquid into another glass.

Now pour the clear decanted liquid into the calcium chloride solution with stirring. Within seconds, you should see sparkling needles rain out of the solution. These are your crystals. The transition is especially striking in direct sunlight. The crystals can be saved and seem to remain stable in air regardless of ambient humidity.

I unfortunately have not seen this demonstration written down elsewhere so I can't offer a citation. I came to it by personal experience when I was on a crystal growing kick as a kid. (Though it may well have been written down somewhere that I have never come across.)

[1] Like in this video: https://www.youtube.com/watch?v=AO67MnZaAvQ