Internet Security, quick questions

Allright, so I'll admit, when it comes to internet security, I'm a little clueless.

Well, to be specific, clueless as to how the threats (that I make sure to protect against) work. I've always just left it at antivirus, spyware remover, and avoided anything too hot.

But, as anyone knows, eventually, stuff gets through. I do my best to remove the crap, and I'm probably going to reformat my computer in the next week or so.

My questions are:

1. After using a spyware remover, adware remover, antivirus, are there threats like keyloggers or information-thieves that manage to stick around? How can I find out if I have them?

2. Hypothetical situation, if there ARE such threats remaining, and I have a new computer (say the one I'm getting for school) fresh on my LAN, can the security problems affect the new computer? That is, if there's a data thief, or something that steals passwords, credit cards, etc. on THIS computer, can information entered on my new computer be stolen?

I know it's probably sounding like a dumb question to some people, but like I said, at the moment I'm a little uneducated, so I was just checking to see if anyone had a quick explanation for me.

Thanks in advance.

How ya doing, buddy?

Allright, thanks for the info guys, I appreciate it.

There's nowhere I can't reach.