Without considering security at all: web browsing, today, will not be a good use of a 700MHz G4 that only has 512MB of RAM. It just won't work well, and there are honestly loads of things you could do on that machine that it would be better at.
As with Unknown_K, I would be running 9.2.2 on there. At most, I would consider 10.3 on it, to recreate what I had in the early 2000s with my TiBook and blue-and-white G3, but I'd want something a lot faster to use 10.4 or 10.5 on. 9.2.2 though, will be fast enough to do some multitasking with simpler software, or to do some neat things with some of the higher end OS 9 software for technical computing, content creation, etc.
But, this thread has been running almost ten days as of this writing. You could have installed 9.2.2 alongside every version of OS X that will even run on this thing and given it a day or two of trial under your own proposed workload by now, so at this point, I'm not sure how productive any more responses to the thread will be, whether or not they are "on topic".
At this point, I would say that if your goal is to browse web sites, you "absolutely must" upgrade away from a 700MHz iMac G4. I don't think, compared to your G5, you'll notice 10.5 or 10.4 being appreciably faster. (And, like I said, it's been a few years since cell phone passed the G5 Quad in overall performance.)