Just for a bit of context I was “surfing the internet” in 1994 via Gopher, an early alternative to the web as we know it now and I used it primarily to find and download apps stored on computers connected to the internet.
In 1995 I was using the Mosaic browser and later Netscape to surf the World Wide Web mostly via webrings that were individual webpages that had links to other wepages of similar content linked to them.
I don’t recall and am not aware of anything that would resemble a meme from that time? This is a year or so before Dancing Baby which is usually considered the first viral video and even then that was originally shared via email forwards.