I will start by saying that of course you shouldn’t do anything you are not comfortable with doing. Especially if you are going to be leaving it unsupervised.

On the raspberry pi the headers allow you to insert wires directly into the board. Those are I/O pin headers, the black blocks with the holes.

As the simplest option you would just strips the ends of the wires to get the bare copper and push them into the holes.

Simple example tutorial on raspberry pi site.

Next best would be pins that you can crimp onto the wire. Pinch it to the wire with pliers doesn’t have to be too fancy just needs to fit snug in the holes so it doesn’t come loose. You can actually purchase wire that have these pins attached. You can find them by searching for bread board jumper wires as an example.

Keep in mind that the raspberry pi board is limited to 5v on the output so unless you plan on adding secondary power you are limited in your LED selection based on the output voltage of the pi board.