Not sure how your original tracks and data were recorded, but if they are as GPX files then the key might be to leave them as this rather than trying to turn them into anything else. If not, then perhaps export as GPX. GPX does a good job of storing tracks in particular. What's important about a GPX track is that it's a record of a set of readings of point locations taken in order. It's the software you view a GPX on which decides how to display this - ordinarily with a set of lines joining the point locations.
QGIS is very capable of working with a GPX file - you can do many things with it, but it's difficult to find a better way to store the information than in the original GPX file. Once you mess with other formats you may end up with lines and points and all sorts, but this format is specifically designed to record a journey (or planned journey) and other formats will probably be a compromise.
Thereafter the key to keeping track of your records may not be anything to do with the GIS software (or anything to do with layers), but other things. There's plenty of scope in a GPX file to store additional notes or information - quite likely added carefully with a good text/xml editor. With this and a combination of carefully chosen file names, and/or a good filing structure, you have an excellent way to store your archives. This means you are then free of any particular software, using a well established text based file format and other obvious methods to store/archive your information.