How to select hardware for my Arduino board? As I embark on my first Arduino project, I have lots of questions. Specifically, what considerations should I make when selecting equipment, and what are the critical parameters to safe operation?

Some elaboration upon my questions can be seen below. However, outlining general principals of equipment selection would be highly useful. 

I have an Arduino Uno. The Uno has an input voltage of 6-20&nbsp;V, and operating voltage of 5&nbsp;V as from the tech specs. Does this mean that I can select any sensor with less than 20&nbsp;V output to send data to my Arduino?

I am interested in using a sensor like this
 Texas Instruments HDC1080 High Accuracy Digital 
Humidity Sensor, which has a supply of 5.5 V. If my logic is correct, this output should be fine. I should know whether or not I need to buy some sort of shield based purely upon the output pins of the sensor, correct? I know I have 6 analog and 6 PWM/digital pins on the Arduino, so the digital signal should be capable of being processed by my Arduino. However, the interface type on the sensor product is I2C, but I am unsure as to what this means or if it needs to be a consideration.
For your first project, power the Arduino Uno with the USB cable and use everything at 5V.
There are tutorials which guide you step-by-step to make something. The Adafruit tutorials are very good.

The HDC1080 is a sensor that works at 3.3V and at 5V. That means you can use it with the 5V Arduino Uno without problem.
This Tindie HDC1080 module points to a HDC1080 library on Github. I suggest you try to make that work.

If you can not get data out of the sensor, then you should start with something very simple. A few leds (with series resistors) or a LDR light sensor is fun to start with.

As soon as you start using higher voltages (for example 12V) you might consider buying a spare Arduino Uno, because the Arduino Uno will be blown when 12V touches one of the pins.

Be also careful with sensors that can only handle 3.3V and not 5V. Since the Arduino Uno runs at 5V, a pin of the Arduino could feed 5V into the sensor and damaging the 3.3V sensor.