Generally use cheap (kitchen) sponges for washing down with cheap bulk bought citrus degreaser. Throwing them away when they're getting tatty/unwashable. Avoid ones with scoring pads!
I use same citrus degreaser (it's an industrial floor cleaner, around £26 for 10L) neat in a chain cleaner (as it's not as 'strong' as the cycling branded stuff that's 100x the price). Generally wiping chain down with old rags (tshirts, pajamas, jeans etc) first & after chain cleaner, rather than buying specific cloths for it. I'd probably use j-cloths but the blue dye in them would probably come out with degreaser?
Once chain is clean & lubed I wipe excess off with kitchen towel or mechanics blue roll carefully so it doesn't shred & end up in my drivechain.
Buying cheap nitrate 'work' gloves was probably the best investment. I get them cheaper than this through work.
