Firstly and perhaps most obviously, you need to get your files off your old devices and on to somewhere new—preferably in two new separate places (like another computer and the web) to make sure if one backup fails you’ve got another in place.
If you’re already using apps and services that are based on the web, like Gmail or Netflix, then you can relax a little—all your content will be waiting for you on the new device the next time you sign in.
For those not using web-based services, there are several ways to save your data. Programs like Dropbox, Google Drive, CrashPlan and Backblaze will all put your files in the cloud for you, but plans large enough to duplicate your entire computer will cost anywhere from $50-$100 annually (the most expensive plan, Google’s $30 TB/month, costs $3600 annually). Or, you can invest in an external hard drive and simply copy your files over from your device—though it may be worth getting a second hard drive as a fail-safe in case one gets corrupted.