It is suggested in many treatises to parents of youngsters (use your own definition) that they should never have unsupervised access to the internet. This can be onerous, and in fact virtually impossible where they have access to a smartphone. But, it is a good idea to keep computers in an area where they can be seen - ie in a family area (not in the childs bedroom). Laptops may pose a problem, but it is possible to weaken the wifi of your broadband router that reaches upstairs rooms.
Always use an anti-virus product, whatever operating system you use, and there are competent free versions available. You can access these packages either by following the link shown or typing it yourself in your browser. If you know the web site address (URL) it is preferable to type a web site address rather than use a search engine, and subsequently bookmark it. Some search engines (even very well known ones) have been "poisoned" for hackers and you may end up somewhere other than where you wanted to.
Antivir - http://www.free-av.com/
AVG - http://www.avg.com/
Avast - http://www.avast.com/en-us/index/
Kaspersky (no free offering)
Microsoft Security Essentials - http://windows.microsoft.com/en-US/windows/products/security-essentials
Norton (no free offering)
Bitdefender - http://www.bitdefender.com/solutions/free.html
Reviews rate the free versions of AVG, AVAST, BITDEFENDER very well and MSE well, almost on as good as paid for software. The MS package has a small footprint and is unobtrusive. Paid for versions offer significant additional facilities. Currently (Nov 2016) the best paid for package is Kaspersky.
Never follow a link offered to you from an unsolicited email or web page.
An additional warning, if you receive a phone call from someone suggesting they are a Microsoft partner and telling you your computer is infected, or corrupt, etc, ignore it (although you may want to take advice - but not from them). They wish to plant software that will enable them to access your computer remotely and either steal your financial details, passwords or use your computer to send spam. Their motives will not be in your interest.
If you're feeling neighbourly keep them talking and ask them which computer etc, and should you become bored, you can finally tell them your computer's operating system is Linux, or alternatively that you don't have a computer!