When dirty, and only when dirty - like lots of riding in wet weather - I have given my drive train and bike a quick hose down, then bring it inside where I continue wiping it down and do a general detailed clean-up. I remove the cassette and wash it with Simple Green. I clean the chain with a spray solvent like WD-40 or similar. Then put it all back together and re-lube with a 50/50 mixture of Duralube (available in automotive store) and mineral spirits. I hit the derailleur mechanism joints and brake joints with a quick squirt of spray lube/protectant like WD-40 or similar. Wipe off any excess. About anything works. My bike rides and looks brand new after this.

For general wiping and cleaning, I use standard bathroom type wash rags that you can buy at Wal-Mart for litttle or nothing. I think you can get about 20 rags for a dollar or two. Some can be washed and reused, but the greasy or dirty ones I just throw away. They are not expensive. Lemon Pledge wipes that you can get in a grocery store work quite well too with general clean-up.

As has been stated, go quick around the BB and hubs. I like the milk carton with hot water idea too as a first pass cleaning vehicle. This precludes "forcing" water which can cause it to enter areas that it probably should not (BB and hubs). At the same time it provides a good cleaning vehicle since the water is hot. Put the carton in your microwave to get it hot if necessary.