Best container to move prized records between homes? Thanks!

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).

I used standard small heavy duty moving boxes and moved them in a UHaul. 95% of furnishings professionally moved.  Then again, I drove 1500 miles without stopping to sleep.

U-Haul Boxes either regular or heavy duty.  Each record size box will hold about 100 LPs.  Then then are HEAVY.  I would suggest you use a pallet.  You will be able to fit 12 boxes per pallet.  Wrap with cling wrap and short of the truck crashing and burning, you should be 100% protected.