That's up to you. Most bikes are much more capable than their riders - me included so absolutely no offense intended. Your riding skills have to progress at a rate that is right for you. Don't let *ANYONE* tell you that you need to wear your tires to the edges. That may or may not happen in your case depending on your riding style especially on the street. Remember that the limits of traction vary depending on many factors including road conditions (wet/dry, sand/gravel, etc.)Just got back from hitting my favorite twisties again. Still can't bring myself to push it. There is little less than an inch of tread on the outsides of my tires that looks brand new. Therefore, I think I can still lean it over a bit furthur (Or can I?).
The track is a much better place to explore your and your bike's limits. For some real fun, find a novice track day event to attend especially if they offer instruction/coaching.