I'd be a lot more subdued when it comes to the killings and avoid doing ANYTHING to gather attention.
Light's biggest problem was his pride. It's not that he was stupid, but he was so arrogant that almost everything he did reeked of "I'm superior to you" and it was clear that he was the type who would buy into a challenge to prove his worth. The fact that he wrote Lind L. Tailor's name pretty much proves this. I originally dismissed it as him making an idiotic move, but the fact was that he has so much arrogance that for him it's worth it to go that route for the sake of proving that his ideals are correct.
Me? Not so much. I'm no lawful good person but I personally would only go after the truly evil people in his position, and on a much less regular basis than Light. It got to a point where Light just began killing the people who pissed him off and it not only made me dislike his character but it was also where Light's worst mistakes come in as well. He did many, many unnecessary things for the sake of his pride and in many instances he could've avoided trouble had he not done so. Had he just ignored Lind L. Tailor as some guy who just didn't like what he was doing, then L probably wouldn't have pinpointed anything about him at all. Further beyond that, Light killing Raye Penber pretty much gave away the fact that the guy had encountered Kira and, if anything, made Light all the more suspicious.