I've been hit by the Partner18mydomainadvisor malware...

[elija]

It sounds like you hit by a malicious javascript. Use Firefox on both computer and install the Noscript security suite add on to protect yourself. It disables all javascripts and allows you only enable the one you need on sites you trust. You should avoid enabling third party scripts where possible.

For a search Engine, I used to recommend startpage.com as they respect your privacy and use Google but it looks like Google may be messing with results returned to it based on my entirely unscientific experiments. Now I recommend duckduckgo.com