For this particular image, I used the red, green, and blue channels to pick one channel to use, then I edited it slightly more with the channel mixer adjusting the red green and blue source channels.
I suspect that this photo looks second best of the three. It seems slightly too dark in the background to like very much. I realize now that it needs a green tone down for an ideal image.
This photo is definitely my least favourite of the bunch. I resulted in this by usage of the black and white button that gives you the channel mixer to adjust. However this channel mixer is different then the one mentioned previously. This channel mixer gives the user the option to adjust reds, yellows, greens, blues, cyans, and magentas!
Despite all these options, it still looks awful unless you're going for a garbage look. I dislike how the flower looks burned and crisp like it was baking at 5130 degrees.
Very ironically this is the photo I prefer although I used the grayscale converter located in image/mode. This choice gives you no say in what comes out the other end. After one presses the button then photoshop will poop out what ever. I admire the appearance because of the range of black and whites. The last two have been too light or too dark, this one is similar to a combination of the previous.
This is the black and white + one colour photo. The photo that is basically the best looking back and white/ grayscale combination with one other colour. I removed the black and white layer partly to get the flower's colour out, I also used a filter to get the yellow much brighter and vibrant. I believe this works well because the flower is to the side a bit thus it's not too boring in the middle. That is all.
Thus photoshop has many choices for grayscale and how you get it, use whatever feels best.