The days after a death belong to the people who are grieving. A monument does not have to be chosen before the funeral, and it does not have to be chosen in any particular week. Many families wait until they can think clearly. That is a sound choice, not a delay you have to apologize for.
When you are ready, the useful order is simple. First, confirm where the person will rest and what that cemetery allows on the lot. Upright headstones, flat markers, and slant markers are not interchangeable in every section. Size, material, and foundation rules are the cemetery's, and they come before a design you love.
Next, decide who the stone is for. A single name, a couple, or a family surname changes the width and the inscription. Ordering a companion stone while one person is still living, with one date left open, is ordinary. The open date is added later, in the same lettering.
Then choose the granite and the words. The name and the dates come first. An epitaph, an emblem, or a portrait can wait until the words feel right. On this site you can personalize the inscription and see it on the stone before you order. The monument is produced as that design shows it.
The cemetery reviews the design against its own rules. After that review, the stone is cut and lettered, and setting is scheduled with the cemetery. How long each step takes depends on that cemetery, the stone you chose, and the time of year. This page does not promise a delivery date. When you order, ask for the timing that applies to your cemetery and your design. That answer is specific to your order. It is not a number copied from a guide.
Some families begin soon after the service. Some wait until a final date is known, until another person can decide with them, or until a later season. All of those are valid. The monument is not a measure of how quickly you grieve.