For pre-1871 baseball, the most complete research site is Protoball (
https://protoball.org/Welcome_to_Protoball). You'll have to dig around for various teams & players.
I have a thread in there that's fictional with some real elements that starts in 1857:
https://forums.ootpdevelopments.com/...d.php?t=350846, real in that I used some team names from the time and one real-life player. Otherwise all made-up, but it was able to conceive of it using resources like the link I've posted.
Some well-known teams from the period include Atlantic (Brooklyn), Mutual (NYC), Excelsior (Brooklyn), Knickerbocker (NYC/Manhattan), Eckford of Greenpoint (Brooklyn), Athletic of Philadelphia, and Union of Morrisania (NYC area).
A larger list of the earliest baseball clubs can be found here -
https://mlb.mlb.com/memorylab/spread...iest_clubs.jsp - but the link doesn't seem to be working for me right now.
A one-stop page containing information about stars of the 1850s & 60s doesn't really exist as far as I know, so you'll have to probably do things like use Google and look up the National Association of Base Ball Players on WikiPedia. One potentially good resource might be this link:
https://www.19cbaseball.com/players.html