Yes it will work in your walkman and home cd player. (assuming your burner has no problem with them, and your walkman and home cd-player don't either. The ability to play on various cd-players depends greatly on the quality of the media and the whether your burner 'likes' them)
Depending on what standalone it may be a different case. If it's the home music/consumer type of cd-recorder stand-alone, they use 'special' consumer audio disks for recording (more government, whining artists and tax grab BS). I assume they will playback computer cd-r's but I'm not positive.
Some standalone units like the HHB Burnit will burn on consumer audio and plain old cd-r media.