I know nothing of the bare knuckle era bar John L and would like to hear about the greats of an alien era to me.
Read about Daniel Mendoza, Bill Richmond, Henry Pearce, James Belcher, Tom Cribb, Tom Spring, Tom Sayers and Jem Mace.
By bare knuckle I'm guessing you mean pre-Queensbury Rules. Favourite of all time is Tom Molyneaux. Then we have Hattie Stewart, Hattie Leslie and Cecil Richards probably the last batch of fighters to be world heavyweight "championess", but details are pretty sketchy. And of course Daniel Mendoza. Liz Strokes, has an awesome story and was a mouthy trash talker to boot.
Jem Belcher was probably the best heavyweight bareknuckle (maybe Sullivan but he was much more a gloved boxer). I don't know enough to say P4P. Dutch Sam, Jack Randall, Nat Langham, Tom Sayers, Jem Mace would have to be considered I believe. There's a couple earlier ones who are said to have been very good. Death (Stephen Oliver), but there's very little on him, and George Ring was said to have been influential to Humphries, Ward and Mendoza, but otherwise I've only found a couple references.
As far as I know, it wasn't until London's The World around 1787 that boxing started get better coverage. The publisher was Vincent Dowling, the father of future editor of Bell's Life in London.