Vinyl records warp from heat and pressure, and stacking them flat is the fastest way to ruin a collection. The golden rule is to pack them standing on edge, exactly as they sit on a shelf, in small boxes you can actually lift. Keep them upright and cool and even a large collection survives a move in perfect shape.
Pro tip: Small liquor-store or book boxes are the right size and strength for records.
Watch out: Never stack records flat. The pressure warps them permanently, especially in the middle of a stack.