Either way is absolutly fine, there is no faults in any way that you put the Wii (unlike the Xbox 360, which tends to scratch disk if standing up straight). However, when choosing which way to put it, you may want to consider this:
Space, the one thing the Wii needs to breath. Take note that if you lay down your Wii, that one of the vents actually are on the bottom. So if you do lay down your Wii, make sure its on a solid surface (not on a carpet or else there will be no breathing room). Same thing when you stand the Wii up, don't have the vents right next to another piece of equipment that emits heat. Give your Wii some room, about 2-3 inches (3-4 centimeters).