A few quick tips on why newly planted cacti die.
If a cactus stays wet too long, it will start to rot. The roots die and the plant will get discolored and soft. If you catch it early, you can save the plant by allowing to thoroughly dry out. Re-time your watering to allow the soil to become completely dry between watering. Recently one of the prickly pear pads I tried to root rotted instead.
Cacti love the sun. But a new plant from a greenhouse was definitely grown in complete shade. Exposing it to a full day of bright sun can scorch the cactus’ skin. You can harden it off by leaving it under a tree that gives filtered sun. Or you can plant it and provide shade, gradually decreasing the shade until it can stand the sun. I don’t buy shade cloth. My cheap version is… a paper towel! Ta da! Paper towel shade cloth gradually wears off over time, allowing the plant to harden off.
Not all cacti can be planted and forgotten. All newly planted cacti should be watered regularly the first year to get them established. I don’t water more than once a week and not less than once every two weeks.
Once established, monitor your cacti and you will be able to tell if they are getting stressed from lack of water. Prickly pears get wrinkly in the summer without a drink (once every 2 weeks keeps them very happy). Cholla never need extra water once established. I water saguaros regularly to encourage growth.