Having recently read through all of the early Arthur books, I've managed to track down the first appearances of most of the characters. Enjoy!
Arthur (Arthur's Nose, 1976), Buster (Arthur's Eyes, 1979), Francine (Arthur's Nose, 1976), Fern (Arthur's Eyes, 1979)
Brain - definitely (Arthur Goes to Camp, 1982), Brain - maybe (Arthur's Nose, 1979), Binky (Arthur's April Fool, 1983), Sue Ellen (Arthur's Valentine, 1980)
Muffy (Arthur and the True Francine, 1981), Bailey - maybe (Arthur and the True Francine, 1981), The Crosswires - Chip, Ed, Millicent (Arthur Goes to Camp, 1983), Pal (Arthur's Pet Business, 1990)
Jenna - maybe (Arthur's Eyes, 1979), Prunella (Arthur's Teacher Trouble, 1986), Alex - maybe (Arthur's Valentine, 1980), Maria - maybe (Arthur's Eyes, 1979)
Ms. MacGrady - probably (Arthur's Chicken Pox, 1994), Mr. Sipple (Arthur's TV Trouble, 1995), Carl Manino (Arthur Writes a Story, 1996), The Tree House (Arthur's Valentine, 1980)
The Reads - Jane, David, D.W. (Arthur's Nose, 1976), The Reads - better detail (Arthur's Nose, 1976), Kate (Arthur's Baby, 1987), The Tibbles (Arthur Babysits, 1992)
Mr. Ratburn (Arthur and the True Francine, 1981), Mr. Haney (Arthur's Eyes, 1979), Ms. Sweetwater (Arthur and the True Francine, 1981), Bitzi Baxter (Arthur's First Sleepover, 1992)
Things have really changed over the years.