Once you have your files off of your old digital media, you will need to consider how to preserve, find them, and access them in the long term. A good place to start are the steps outlined in this personal digital archiving handout [PDF] from the MIT Libraries.
The MIT Libraries data management services team also provide good guides on how to store and document all types of your data from the past or present, and ways to add information to them so you can easily find them again.
Hopefully after transferring and setting up good management and preservation practices for your files, you'll have access to your data and memories well into the future!