The two pictures above are identical, neither have had different processing except that they were saved with different color profiles. On the left is the “Adobe RGB (1998)” color profile Photoshop uses by default and my camera is currently set to shoot. On the right is the same picture that was converted to sRGB then saved and uploaded.
Adobe is actually a wider color range than sRGB but the internet runs on sRGB so it can’t render all the pixels and the Adobe shot doesn’t look as good (in this pic it looks less red). When you look at the lefthand shot in photoshop it looks basically identical to the sRGB shot (technically it has more colors but most people can’t tell at a glance). So the irony is that the more limited sRGB shot on the right is what I saw while processing the image, but when I upload it without converting it to an internet friendly profile people don’t see it the way I intended and the “limited” profile looks better.
The basic lesson is that color profiles do matter (printers sometimes use CMYK so there’s one more conversion to worry about). What you choose to use depends on your own personal workflow, you could just set your camera to sRGB and not worry. Personally I shoot in RAW pictures and plan to process all shots anyway so I have more data to work. I just have an action I use at the end of processing that saves a .PSD file, converts the image to 8-bit sRGB, then saves a .JPG.