Pincello has a lot of small components, and your life will be much easier if you can keep them safely stored when not used, but also well organized so you can quickly find what you need.
You will need this cable to both program and provide power to the microcontroller by connecting it to your computer. If the microcontroller is already programmed and you only need to provide power, then you can attach it to a portable charger.
This microcontroller can be considered the central part of the kit. It has multiple General-Purpose Input/Output (GPIO) pins to connect different kinds of sensors and actuators, you can program it with the uncomplicated Arduino Language (C/C++), and it has Wi-Fi, which means it can connect to the Internet.
This is an alternative microcontroller. The Arduino Pro Micro is based on the Arduino Leonardo board. It has no built-in Wi-Fi, but the ATmega32U4 chip allows the microcontroller to be natively recognized as a USB keyboard and/or mouse. For instance, you can make use of collected sensor data to send specific keypresses and mouse movements to a connected computer.
Electronics can be tricky (and expensive) if you have to solder connections everytime you want to test an idea. A breadboard is designed to prototype circuits without the need of soldering, and this one will accommodate not only your circuits but also the ESP8266 NodeMCU 1.0 Microcontroller. For more information about breadboards, this tutorial can be useful: How to Use a Breadboard.
To connect circuits on a breadboard, you need jumpers (which are wires). You can use any available jumper to make your circuits. However, a rigid jumper is a bit more practical for prototyping because it already comes in convenient sizes and can be easily and sturdy placed on a breadboard.
Resistors are needed in circuits for many reasons. For instance, their correct use prevents damage to sensitive components such as the microcontroller. In Pincello, this particular 330Ω resistor will be used in LEDs (both single color and RGB). For more information on resistors, this tutorial is recommended: Resistors.
Another use for resistors is to control how energy flows in your circuit (always through the path with less resistance). In Pincello, this particular 10kΩ resistor will be used with push buttons to control high and low states. Again, for more information on resistors, this tutorial is recommended: Resistors.