My mother died in September, so things have been a bit hectic since. The good news for you all is that I've managed to learn a lot about saving costs when someone dies.
First off, it makes sense to pre-pay your burial expenses. The very simplest burial cost my family well over $15,000. However, you can either invest money in something like a CD to pay for expenses in the future, or pay out over months or years if you prepay.
You are not required to buy a casket from the funeral home. Caskets on Amazon, as of this date, start at about $900, and can be shipped directly to the funeral home, and the funeral home must accept the casket and use it without any further charges to you. A simple casket from our local funeral home cost $2,500.
As you choose where to be buried, understand what fees there may be for the burial. My family paid $2500 just to open and close the grave. We still haven't bought the headstone.
If you choose cremation, what will happen to your ashes? And if you choose to donate your body to science, again, what will happen to the remains?