Naval jelly will remove rust but not prevent future rust. For that you need to wax it once or twice a year, depending on use and exposure to moisture. For the painted rims, don't use naval jelly (it will also remove old paint) but rather make a bath of oxalic acid (google Bike Forums Oxalic Acid), then protect the cleaned surfaces with wax.

Get that thing all shiny, and your daughter is the coolest kid on the block, come July 4.