Think of it this way. In my example if your vf (forward voltage) of your LED is 3.1 and you use 3.5 volts to power your LED, then you need a resistor to make up the .4 volts to balance the circuit. To find the correct resistor you would use Ohm's Law. For simplicity sake you can find Ohm's Law calculators online to get the correct value resistor for your application with a Google search.
I didn't fully read the description before. If you use the LED you linked in your original post you only need a resistor. Typically you would need a cricuit or driver to do that but this is much simpler. As for your power source, like I said you want as close to the forward voltage of the LED as possible because then you can use a lower value resistor. Since LED's require more current and less voltage the more voltage you pump into your LED, the more resistance you need to balance your circuit. Then you get into the more complicated matters of heat management for your resistor and LED and that's more complex that what you need for your set up.
I hope that makes sense. It's been a number of years since I learned this directly from my late step father who taught me all about it. He was an electrical engineer and in the last few years of his life worked for an LED illumination company. Plus I've been building in hilt LED lightsabers for almost 20 years.
I hope this helps you out!