If you suspect problems, loading an anti-virus might not do anything. Many malwares and viruses block the operation of these programs. I believe that W8 came with Microsoft Security Essentials as a default. I am not sure as I avoid it at any cost.
Having said that I would run a few programs to see what they find. The first is MalwareBytes:
https://www.malwarebytes.org/then Superantispyware:
http://www.superantispyware.com/then an anti-rootkit:
http://www.sophos.com/en-us/products/free-tools/sophos-anti-rootkit.aspxthen install an antivirus program, my personal favorites right now are MS Security Essentials and AVG. Neither are perfect but do help with some things. Run MalwareBytes and Superantispyware semi regularly to keep an eye on things and you are pretty well protected. If things seem to be running weird still, then some of the system files and permissions might need resetting. The best way I have found for correcting system problems in Windows is a program from tweaking.com called All One Repair:
http://www.tweaking.com/content/page/windows_repair_all_in_one.htmlMost people with computer knowledge will start screaming about anything that does things in an "all in one fashion", and I was skeptical about this one too until I ran it out of desperation with a problem I couldn't fix normally. It does help in many situations.
Other things to do? As suggested, run users with restricted accounts, run Firefox with NoScript, Ad Blocker Plus, etc. This keeps pages from loading scripts and redirects without your knowledge. A restricted account is an account for the user with their own password that is not an admin account, and can have restrictions applied to what files that can be seen and/or changed. These settings can be found in the Users Settings in Control Panel, or whatever MS calls these things now with W8.
Oh one more thing, expect as many different opinions on what you should do as replies you get to your question.