I use Genesis from OS3.9 CD to connect to the Net, and for web-browsing I use Voyager, which has SSL built-in. I haven't really tested out thoroughly its usefulness regarding SSL, as I use my PC for that, however I've tried it once and it worked, to my amazement, with my web banking account.
Voyager crashes a lot with non-RTG modes (AGA for example), but is very stable with video cards.
