Yep you will have to draw out a diagram of the LED's and use a resistor calculator to figure out what value resistor you need.
Build and test your circuit before installation. I speak from experience. Finding out your LEDs are wired backwards after you hot glue them in there is not good hahaha
Dust is not a big concern. Worry about short circuits because that could damage the power supply, or worse, the motherboard. When you take the system apart try not to drop stuff onto the motherboard because it might cause a short circuit when you power it on.
Just keep your wiring color coded and organized... i use yellow as +12volts and red +5volts... black is my ground.
Personally I would feed my mods' directly from the motherboard's power supply connector because there is almost no chance of loading down the major system components.
Good luck bro you're in safe hands.