To secure your Internet connection set your home router or personal computer to use OpenDNS Home, FamilyShield, or Home VIP. OpenDNS makes web browsing safer by filtering out phishing and other malicious sites, it speeds up your browsing experience, and it allows you to customize the filtering for of objectionable sites. If you're a techie you may also want to check out DNSCrypt for Mac and Windows which further protects your online communications which may be of special concern when using unsecure Wi-Fi.
Security works best in layers so don't rely on just one form of protection for your computer. To that end be sure to keep your computer updated with patches for the products you use. This is especially important for Adobe Flash and Oracle Java. To help with the task FileHippo.com provides an update checker for Windows and AppFresh provides a similar tool for OS X.