There is one thing that bothered me about your question:
"..But the only programming language I know is Java."
So learn another one!
Anyway, Java as a client in the browser fails on many, many fronts.
For one, Java 7 (and most likely Java 8) doesn't even work in Chrome on Mac OS X because the Java people decided to stop supporting 32-bit, and Chrome is a 32-bit browser. To me this speaks volumes about Sun/Oracle's attitude towards supporting "every system" like they have claimed in the past. So right off the bat you have these compatibility problems with Macs and older systems, requiring workaround. So much for "write once, run anywhere".
I really think you're better off either building a native client, or using HTML 5 (if it will be a simple browser-based game) or using Flash instead. Flash is much more proven as a multiplatform, in-browser tech that works. Realm of the Mad God was programmed using Flash, as well as oodles of newgrounds entries.
Here's to not seeing that godforsaken java cup on any new games