Nice choice with the Ice Wax. It's by far the
best chain lube I've ever used. Just remember this: as enticing as it may be, do
not put in on pumpkin pie! It's not nearly as good as it looks. Yuck!
As for cleaning my chain, I just get a rag wet and soap and back pedal the crank while I hold the rag around the chain. Then I get a clean rag and do the same thing to dry off the water. Then lube it with the Ice Wax and you're done. If you want to really clean the gears, it's best to just go ahead and take them all off and scrub them individually with soap and a scrub brush.