One often-quoted rule of thumb about colour wheels, for those that find them useful, says that you usually don't want the exact opposite colour, but something around 120 degrees to either side of your first pick. This still gives good contrast but not quite as strong and potentially vision-destroying as the directly opposite colour. Lightness of the hue makes the issue a bit trickier, though, and any decent physical colour wheel available from artists' supply stores has the lightness built in as a radial component (plus a stencil for convenient viewing of pre-determined colour pairings/sets without interference from adjoining shades).
Of course, rules of thumb are rules of thumb, the neurological and psychological aspects of human colour perception tend to get quite complicated at times, one's artistic vision may vary and a colour wheel is ultimately just a tool for keeping the classic concepts of colour harmonics in mind.
