I check wine with Delta frequently. When travelling with any significant quantities, I use wine shipping boxes available from wineries or brokers in the business of shipping wine. The shippers have styrofoam or cardboard forms that protect the bottles. If I have the opportunity, I will also stop by the package-shipping stands at airports to have the box cellophane wrapped, to ensure it to does pop open (a lot of tape also does that trick, though with less assurance) and to protect the box's outer cardboard from dampness/rain on the ramp. At SFO, for example, I stop by the international terminal for package wrapping before heading to the Delta terminal.
If I'm going to a place from which I plan to bring wine home, I generally bring an empty shipper box with me, fill it up, and check it as described above for the way home. May sound nuts, but it avoids the hassle of finding the shipper box, which can be a problem in some areas.
Never check wine in the cases that you see in liquor stores. The cardboard is just too flimsy, liable to popping open or letting the bottles get knocked together. I was sorry to once see a fellow pax at baggage claim at SFO receive a case of Aussie wine all broken up in the bottom of one of those bins for loose bags (this was a UA flight from SYD). I've seen lots of other pax at ATL receive the shipper boxes without incident at baggage claim from SFO. Once in SFO I even saw another pax collect an empty shipper box at baggage claim inbound from ATL-- proof that I was not alone.
For those who travel with significant quantities of wine, the shipper boxes are essential.
When I'm travelling with somewhat smaller quantities or trying to be more discreet, I generally put the bottles in those neoprene carriers by NY Built, then surround them with gym clothes, put them inside old shoe boxes taped closed to prevent shifting in transit, then put the boxes in the lower part of my stiff-side regular luggage (B&R). This has worked well for me.
Liquid restrictions are a hassle. But workarounds are available for oenophiles. Good luck.