There are SO many ways to change to b&w... the "right" was is whatever looks good to you. This is what I tend to do:
go to the channels palette and look at the red, green, and blue channels. take note of the one(s) that look the best to you. You may like one part of the photo in the green channel, but another in the red.
then I change the mode to LAB color and look at the lightness channel. sometimes that looks the best to me. select all and copy. undo until you're back in RGB mode, then paste.
with the background layer selected, copy and paste the color channels you like.
you can play with the blending modes, opacities, and layer orders of your b&w layers until you get something you like. I'll often mask out some parts, maybe duplicate a layer, and I play a lot with the blending modes.
I find that doing this gives me a lot more control than the channel mixer, but it takes a lot more time, too.
I tend to do everything the complicated way.
but I'm crazy like that.