Those LEDs will work. You need wire and depending what LED controller board you have, you may want connectors. If you don't have a controller board, then you can wire them straight to power tapped from the computer, but I have to admit I have never done that so someone else will have to reply.
There is a diagram here: http://support.paradisearcadeshop.com/support/solutions/articles/14000026298-5vdc-rgb-il-lumination-diagram
To get a red LED you solder just the red corner to one wire and the corner labeled g (where the power comes in) to another. For a blue, the blue and the g. For purple, blue AND red and the g. All four corners will get you white or RGB control, depending on how you connect the other end of the wires.
The other end of the wire plugs into your LED controller board. If you are doing single color, you connect only that wire to one terminal, and the g wire to power. A combo color like purple, you connect BOTH color wires to one terminal, and power to the g corner. For RGB, you connect power to g and each of the three colors to a separate terminal, and in software (such as LEDBlinky) you tell it which terminal is red, green, or blue. Then you can assign the relative levels of each to make all the colors.
The LED controller may use any of several different methods for connecting, though. Some use screw terminals, some use header pins. If it's header pins, you probably want to add connectors on the end of your wires, it makes life much easier.
If you have space on the controller board, I'd wire all of them and use software to set the colors; it's less complicated wiring, really.
To wire up a Pele ring, you go through basically the same process.
PS, I apologize, I may be the person who bought out the pre-wired LEDs.