There are 2 parameters that you will see quoted. Luminous flux (usually measured in lumens) measures the total amount of light emitted by the LED. For reference, a 50W halogen bulb emits around 800 lumens.
Radiant intensity is usually quoted in candela for visible lighting, and mW/sr for infrared emitters. This specifies the amount of light emitted per unit solid angle. So a 50W spotlight and a 50W ordinary light bulb might both emit 800 lumens, but the spotlight emits most of it in beam (specified by half-angle or full-angle, often just called viewing angle) rather than in all directions, and looks brighther (if you look at it down the beam). So the radiant intensity is the best measure of how bright the LED will look, provided that you are looking at it head-on.
So I suggest you look for LEDs with a sufficiently high candela value, and check that the ones you eventually select have a wide enough viewing angle for your application. This http://uk.farnell.com/kingbright/l-154a4surkqbdzgw/led-multi-colour-rgb-5mm/dp/2290374
is the brightest through-hole RGB LED that I found.
That wire you quote is 20AWG, which has a resistance of 0.033 ohms per metre. It will be fine for that application.