DO NOT USE STEEL WOOL. That is a major no-no in drum restoration. But don't be discouraged - a common method is to disassemble all the parts - and soak them in (I am referring to chrome parts) in Dawn (dishsoap) and water - pretty much the same mix as when you would do dishes - maybe a bit stronger. Soak them in there for about 48 hours, then brush up the parts with a toothbrush. The water should start turning green, and indeed will once you brush the parts up (as you brush over the tub, all the dirt and corrosion falls back into the tub). After brushing up - you will be amazed at how good the parts look. But, don't stop there - this stuff is way too easy and can be done in a matter of 3-4 days.
Then, use a micro-fibre cloth and polish with Turtle-Wax Rust Remover and Chrome Polisher. It comes in a green bottle and is really cheap (like $2-3).
It will look like brand new. Wires can be replaced for very cheap and it would help sell the drum if it was complete. You should be able to get 60-100 for this, but don't start bidding (if you auction this) for less than that. starting bid - 60, BIN 100