With regard to the actual move - I boxed everything up, taped up the boxes, labeled them in a way that was inconspicuous but I understood, and packed them up for transport. Since I, ultimately, did all of the pack/unpack for the moving vehicle, I had no concerns about someone else inadvertently grabbing the boxes and opening them.
With regard to storing at your new location and your roommate being "nosey" - if you're going to live with someone, they need to understand boundaries, personal space, and personal property. If they don't, maybe reconsider your living arrangements. Otherwise, you should be able to locate something location-wise that will allow you to stow your items away, out of sight, and where they aren't going to go snooping. Backpack or similar at the back of the closet, above the ceiling tiles in your room if there's a drop-ceiling, or something like that.
If you're not sure about their snooping, maybe get a cheap Wyze camera or something that will store short clips in the cloud and have it in your room for when you're no there to keep an eye on things to see if your roommate is snooping. Do that before bringing your stash into the house.