I would try steel wool before resorting to the wire brush. The wire scratches will show right through your new paint.
I wouldn't strip off the healthy paint. If it stuck to the metal for 20 years without flaking, leave it there, sand it and paint over it.
The bike must stay clean and free of oil and dust when you start to paint. The natural oil from your hand can ruin a paint job. I wipe it with alcohol before every layer of paint.
I preserved the labels when I repainted my Mongoose Zuma cruiser. I masked them and sanded/painted around them.
The labels on my 1976 Western Flyer were too far gone to preserve. Western Flyer head badges are not too difficult to find on EBay.