I am pleased Avast is better than Norton anti virsus software because when i bought the software for Norton it didn’t do the job properly and i have a complaint by mail post that my computer was fifthy full of trojan horses and other such like nasty virsus, i will not buy Norton again also it slowers your computer down into a kerb crawling motion, it took me ages about 1 hour to load a page fron the search engines, i do not recommend Norton.
Keep in mind that NO antivirus can detect everything. No reason to bash other products but glad your happy with Avast. Norton is still one of the best antiviruses as far as detection. Norton users can make a thread commenting that Avast is horrible cause it missed a virus. So on and so forth. The best practice is to have a good backup plan for when the day comes that your antivirus fails you. Do you have a disk imaging software?
Just out of curiosity what did your "first scan with avast find?
Another good tool would be MalwareBytes Anti-Malware (MBAM).
MBAM is great as a stand alone but, for $24.95 (US) you get real time protection.