Using the Channel Mixer is considered the 'best' way of changing an RGB pic into B&W. However, it takes some skill to balance the levels correctly. If in doubt, try to just Desaturate and then play with levels/curves.
Never convert to Greyscale (but I'm sure you don't need me to tell you this)!
I have seen a more complex tutorial on using Channel Mixer - when I can distill the essence of this to you I will.