Gee thats a long time ago. Well after a few years using my Amiga to access local bbs boards that I racked up enormous phone bills on (!) I purchased Miami and downloaded AMosiac and the later iBrowse. This was in 1993 on my souped-up A1200. But as for what I first did... hmm probably create my own home page.
Ps. Wasn't there a search engine back in them days that was maintained solely on the Amigas? I am sure it was around for many years, it wasn't just searching Amiga sites it searched the whole internet just like Google and Yahoo do. Can't remember its name. :S
There was The Amiga Web Directory maintained by CUCUG. In fact, that was one of the first sites I went to back in 1996. I have memories of finding Amiga.org via that site too on my A1200. A lot of my usage on the net at that time was newsgroups and email (circa 96-99)