First of all, I'd recommend you use Firefox as your browser, and just type in/go directly to google.com or clusty.com for searches. You can go to google and download a search bar, if you like that convenience. I avoid Yahoo! searches and Internet Explorer.
I use an old PC (Windows 98!) with AT&T DSL and it works just fine.
I don't know about your particular hardware/software/spyware issues. I have heard not-so-good things about AVG but I don't know that from personal experience.