I am not a big fan of cloud anything- but I think part of that is the fact that all of that stuff is blocked at our firewall at work, so I don't use it anyway. The "cloud" is just someone else's computer. That being said, here is a recipe for safe computing for your family:
1. Make sure that you change all of your router settings from what your ISP has as defaults. That means changing your home network name (SSID) and password, and setting an admin name and password for the management console. If you go to a browser, generally the way to access this is to type 192.168.1.1 into the address bar and hit enter. You can add all kinds of other security features, like listing the MAC address of every device that you want to allow on your network, and blocking unknown devices. I also suggest enabling a guest network with its own SSID and password, especially if your house is the local hub for your kids and their friends. I actually have 2 routers in my house- one is from my cable provider and is locked down pretty tight in our basement (mounted near the ceiling). It only connects to a few devices, including a wired switch that feeds our desktop computers and a few other wired devices. The other is on the main floor, and has dual wifi networks for the family, and a guest network as well.
2. Make sure that you have antivirus software on every possible device and keep it up to date. Avoid phishing and other scams by NEVER clicking on links to websites in emails from vendors you do have accounts with (banks, credit card providers, etc). Instead, go the their actual websites and login there. Scammers have gotten really good at spoofing websites (the recent Google scam is a perfect example), so make sure that you are vigilant at looking at the URLs of any site you go to. If it looks suspicious, stay away.
3. I can't stress the use of STRONG passwords enough. Use different passwords for every account, make them complex Letters, caps, numbers and special characters), don't leave them on a post-it stuck to the edge of your monitor. There are differing schools of thought about changing them often. I am of the opinion that if you have a strong, complex password, you don't have to change it. If you have a lot of accounts that you use often, consider using a password manager like KeePass, so that you have a single password to remember, and it can generate long and complex passwords randomly for each website you need to access. Also, if you have accounts that offer 2-Factor Authentication, pleas use it. If you don't know what that is, it is a system where you enter your username and password (these are things that only you know), and then the website sends a text message to your phone with a code that you then enter for final access (the phone is something only you have).
I'm sure I will think of more things, but start here.