The arduino I linked is like a small brain. You can upload a single application in it (up to 32 KB of binary code) and it will do whatever your application tells it to do.
It has a lot of pins on the side (those black headers) and can output voltage or receive voltage through those headers and tell your application that voltage (either as a 0 or 1 if the pin is configured as digital input or as actual voltage if the pin is set to analogue input)
The 16x2 display I linked to can be connected to a microcontroller or arduino using as little as 6 wires, but an easier mode to "talk" to the lcd requires 10 wires (8 wires to send a character or a command to the screen, 2 wires to tell the display what you're sending to the display). The arduino has 20 digital input or output wires so the LCD will use only 10 of those. When you learn how to use it, you can further change the wiring to use only 6 wires, or even 2-3 wires with the help of a simple 10-20 cent chip (a shift register)
With a connection like those 8 wires for data and 2 wires for other things the lcd needs, the code to use a lcd screen is very easy to understand.. each command (like clear screen, show cursor on screen, blink character, move cursor to a position on screen) is one byte, and you can write a letter at a time on screen by simply writing 0 or 1 on those 8 wires (one byte = 8 bits = 8 wires)
With i2c it's a bit complicated and you need to learn how i2c works, the concept of i2c addresses, then you have to make your own functions to send commands and instruction to the LCD display as a sequence of bits ... with the first you will find ready made code that will be easy for you to read and understand. And that lcd you chose is basically a graphical one, it takes more code to configure it to run then you basically turn dots on and off - if you want to write a letter on display, you have to turn several dots on an off and so on.
I'm not sure that you fully understand this, but these displays are not like computer monitors that you can simply plug into raspberry and have stuff shown on them.
Here's a video that shows how to connect a simple 16x2 or 16x4 display to a home made arduino (jump to 2:40 directly):
This guy has a whole series of videos with arduino that are from absolute basics to stuff more complex, here's the playlist :
https://www.youtube.com/playlist?list=PLE72E4CFE73BD1DE1edit: and by the way, if your parents don't want to buy you an arduino, you can follow the videos this guy made and buy the standalone chip (about 1-2$ on digikey) and a small programmer like the one he uses in the second video in the playlist, which also costs about 15$.