Final answer:
The technician should check the Proxy Settings first, followed by the Temporary Internet Files, when investigating the issue of being redirected to wrong sites. Cookies and Windows Firewall should be checked after the aforementioned settings.
Step-by-step explanation:
The technician should check the Proxy Settings first to investigate the issue of being redirected to wrong sites while clicking on search results. Proxy settings control the internet traffic and can potentially be set up to redirect the user's requests to different sites. By examining and adjusting the Proxy Settings, the technician can determine if they are causing the problem.
After ensuring that the Proxy Settings are correct, it would be beneficial to next check the Temporary Internet Files. These files store website data, and if they become corrupt or compromised, they can cause issues with website redirection. Clearing or resetting the Temporary Internet Files may resolve the problem.
While Cookies and Windows Firewall can sometimes impact internet browsing, they are less likely to directly cause the specific issue mentioned. Therefore, they should be checked after the Proxy Settings and Temporary Internet Files.