Your browser choices in OS 9 are kinda limited.
iCab, Internet Exploder, Netscape, Mozilla and Opera are the only ones I've tried.
I used to use Mozilla in 9, and of course it was slow starting up, but I just never quit the app unless I was short on RAM. Kinda like how Mozailla on Windows is with it's "quick launch," even that how the Mac version works by default.