It would be easy to help with more detail. Rough size? Which gen? how far is the move?
I am very particular about my belongings. Ponies to the largest degree but also everything else in my home. so this is speaking as someone who is obsessive- but applying it to a collection it's a smart move. and most is geared to a BIG move where things might not get all unpacked right away.
Everything I own is packaged, each box has my name/address etc printed on it. Again my name/address is inside the box (if something is lost, I want it back! NOT insurance money). as well as a code. I keep a master list, which lists everything in each box beside the code I have assigned to each. as well as a checklist to I can cross off each and know exactly what arrived and if something does go missing i know right away. My collection is to a degree it has it's own list.
This served me well moving across the country, as well as moving 6 hour drive up island. I had to have it done all at once. I research how to package something if I am unsure. Movers are sometimes not gentle, and ideally a truck should be packed tight, but sometimes boxes can fall, bounce or tossle in the truck. Same thing with inside the boxes- there's a shipping phrase that says "if it moves, it breaks". So anything important, take your time.
If you are doing a very short move, obviously much easier to move important/fragile stuff in your car. and, most climates if a storage unit is needed it should be indoor climate controlled. camping sections even have kits to keep moisture out of campers and boats you can place with your boxes on the floor of your unit. But pony vinyl is sensitive to moister, temp swings, freezing and baking in the summer sun. I've seen some ponies bought from unit auctions, someones shed or attic that were in the most sorry of states (turned brown and splotchy). sometimes it takes years, sometimes damage can happen quickly. = indoor climate controlled storage unit!