I'm on my first build and kind of lost at this point, hoping you can guide me in the right direction.
Based on the buttons linked below, you appear to be going with single-color LEDs, not RGB.
Are you trying for:
1. Always-on. (easy)
2. LED controller board. (medium difficulty)
I'm about to order some led buttons from ebay here : http://www.ebay.com/itm/10-White-5v-LED-Illuminated-Arcade-Push-Button-with-Microswitch-for-Mame-Game-/262547760894?hash=item3d2110e6fe
There are two separate circuits -- button press and lighting.
The button press is handled by the 0.187" QD wiring that came with the Xin-Mo. (NO and COM tabs on the microswitch)
Lighting is powered by 0.250" QD wiring connected to the "saddle stirrup" tabs.
This pic shows "always-on" wiring using 0.250" daisy-chains -- black chain connects to ground, red chain connects to 5v.

You can either buy pre-fabbed daisy-chains (GGG, Paradise Arcade Shop, etc.) or "roll your own" with 22-24 AWG
STRANDED wire and 0.250" crimp QDs.
Ratcheting crimpers are your friend. Solid core wire is not. (Did I mention that you
really should use stranded wire for this application?)
You can get the power from the computer PSU molex (recommended), use a "wall wart" 5v power supply, or (possibly) a USB cable.
LEDs draw about 20mA each, so make sure you aren't drawing too much current for the "wall wart" or USB. (USB spec is 100 mA per unpowered hub port/500 mA per motherboard header IIRC)
Scott