With delivery problems the most critical moment is the moment of delivery. If you saw the package was damaged and signed for it anyway, claiming your rights afterwards gets harder. If the box is crushed, the tape is torn or the weight looks suspicious, you need to open it in front of the courier and, if necessary, have a damage report drawn up.
The second point: the party you deal with is usually not the shipping company but the seller. In distance sales, delivering the product to you intact is the seller's obligation. The order below is based on this.