Hardware Overview
Confirmed Working Hardware
This software should probably be compatible with all Arduino clones and WS2812 LED strips, but I've personally confirmed it works with the hardware listed here:
ALITOVE 16.4ft WS2812B LED Strip
Cost:
$38.00 CAD
$22.88 USD
Amazon links:
Recommended Hardware
You can use whatever you want, but this is the hardware that I'd recommend using for basic setups:
ALITOVE 16.4ft WS2812B LED Strip
Cost:
$38.00 CAD
$22.88 USD
Amazon links:
Recommended Supplies
If you have no shame whatsoever, all you need is a pair of wire strippers or scissors. Some electrical tape would be helpful too.
For more than a barebones LED setup, you might want the following stuff:
Windows Computer
WS2812 RGB LED Strip
Pliers
Wire Strippers
Wire Cutters
Vice
24/22/20/18 AWG Wire
(How to pick wire covered in setup guide)
Arduino
Soldering Iron
Solder
Multimeter
Third Hand Soldering Tool
Breadboard
Electrical Tape
If you're serious about making a cool light setup and you have a spare $100 USD kicking around, Ladyada's Electronics Toolkit has almost all of what I would recommend, plus a few extra things.