Immibis' tubestuff mod adds a Black hole chest which can (very nearly, it has up to 2^31 pages) store an infinite amount of items in it so that is definitively the most compact way possible to store (effectively) all your things. However the configs disable it by default so you would need to be able to edit them to make it available in survival mode.
It has also been known in previous versions to be quite buggy and easily capable of losing all of your items, I don't know whether this has been fixed. The chest is also not sortable so if you stored all your stuff in it you might never find some of it again.
Other than this your next best option for compact storage is an ME Drive, which can hold up to 10 me storage disks for up to 630 item types in a single block, which has the downside of requiring an ME network to connect to but the associated benefit of being able to hide the storage somewhere else and only having a few access blocks visible in your base.
An alternative approach (and the one I like to take after I've got an initial base setup and enough resources available) is to instead of storing all the things all the time just store enough of the things for your (optimistic) near-future needs and have an automation setup that will replenish your stocks as you use them. In short slow down your collecting of all the things so that you don't need as much storage space at once.