Powering LED's?

I’m planning a build at the moment, which will involve using my RPi 2 to run RetroPie whilst being housed in an old PlayStation One case.

To make the “console” look the part, I am planning on making a few modifications that will involve LED’s. For example, instead of the usual green light on the PlayStation One, I am going to replace this with a red one. I am also considering additional LED’s as a way of backlighting a custom logo that will replace the PlayStation logo on the lid of the case.

What I am looking to do is to power the LED’s using the 5v or 3.3v pin. Nothing fancy, but simply when the RPi is on, so are the LED’s (I am contemplating using this mausberry circuit and connecting it to the existing PSX PSU, but that is in version 2 should version 1 work!).

I’m new to electronics in terms of voltages, ohms, resistors etc. but have been reading this guide which gives me a good starting point, but I was hoping somebody with a little more experience could help.

The LED’s I am looking to use are the red ones here and the key details I gather are:

Supply Voltage = 5V or 3.3V
Forward Voltage = 2V
Forward Current = 20ma

Therefore, is it possible to connect multiple LED’s in a series, and if so, what resistor would I need? I have looked at this website which gives me an indication that I would need a 56ohm resistor and I could only connect 2 LED’s in the series before I require more voltage.

Am I on the right lines? I don’t really want to use an additional power supply if possible.