The summary.
THE THREE THINGS THAT MUST AGREE ON A DEVICE
Address, subnet mask, and gateway.
An address without a correct gateway reaches the local network and nothing beyond it.
PRIVATE ADDRESSES ARE MEANINGLESS OUTSIDE YOUR NETWORK
Quoting one in a support ticket tells nobody anything. Quote your public address.
WHAT PROPAGATION ACTUALLY IS
Not a spreading process. Caches expiring at different times.
Lower the TTL well in advance of a planned change, and raise it afterwards.
WHERE RECORDS MUST BE ADDED
Wherever the nameservers point, which is not necessarily where the domain is registered.
Adding a record in the wrong place and seeing nothing change is extremely common.
BEFORE CHANGING NAMESERVERS
Record every existing record first, and create them at the new provider before switching.
Changing nameservers affects mail as well as the website.
THE RECORD THAT CONFLICTS MOST
CNAME. It cannot coexist with other records at the same name.
FOR LONG RECORDS
Copy and paste. A single character breaks mail authentication silently.