i say yes to both. i had the "pleasure" of working for an ISP a while back and you might be surprised at how much spyware, not just viruses, can jack up your internet connection (among other things). i just mention the internet connection as an example... i would spend 30minutes trying to politely explain to someone its not our shitty service that prevented them from getting online, it was the crap on their pc.
that was more of a rant than i intended. so, yeah, to both. ad-aware and spybot are good