Best container to move prized records between homes? Thanks!

Are you moving them yourself in your own vehicle? Not the "best", but the cheapest is the U-Haul small boxes (16-3/8" x 12-5/8" x 12-5/8"). I’ve moved multiple times with those and had no issues.

I added bubblewrap and extra cardboard pieces on the ends and top for additional protection.

I’ve also used the Ultra Box plastic corrugated boxes from Bags Unlimited, but those are overpriced and don’t seem to provide much additional support.

These are all being moved professionally by truck, 1,800 miles across country.
Past experience has been hit or miss that the professional movers pack safely.

When I moved across the ocean, I personally, carefully packed my LPs in cardboard boxes supplemented with LP sized cardboard inserts. I packed the LPs tightly, hoping that it would minimize warping caused by the boxes perhaps being left in the sun as they steamed their way westward to the tropics. In any event, 90% of my LPs went through the gauntlet unscathed, with only a few developing edge warps. If any were rained on, I honestly can't tell.

I bought a pallet of boxes double walled from Bags Unlimited to have about 5,000 records moved across the country. I packed them myself, made sure that the riders on my insurance were up to date value (a blanket for the records) and the movers handled them fine. They went into a high value vault with HVAC at the mover's facility until we bought a house in our new location.

I subsequently found a better box, cheaper, on Amazon- same deal- double walled, sturdy.

Keep in mind that the insurance attached to the standard mover's agreement is pretty much worthless. (Not that insurance would make it easy to replace some of these things but it is certainly better than a loss).