Where you plant it is the whole decision
A mulberry will fruit for you whatever you do. What it will also do is drop several pounds of dark purple fruit, and the birds that come for it will redistribute the stain over a wider area than you expect. On a lawn or in a bed this is nothing. Over a driveway, a patio, a white fence or where the car goes, it is a ten-year annoyance that one minute of thought at planting time would have avoided.
Put it where the fruit falls on ground you do not mind, and ideally where you walk past it daily, because you will eat most of the crop standing under it.
Dwarf Everbearing, and keeping it small
A full-size mulberry reaches thirty or forty feet, which is a tree for an acre and not for a garden. The Dwarf Everbearing we grow stays at six to twelve feet, takes hard pruning without complaint, and fruits over months rather than in one glut. In a large container it stays smaller still.
Prune it in winter and prune it confidently. A mulberry fruits on new growth, so cutting it back by a third does not cost you fruit, and a tree you can pick standing on the ground is worth far more than a tall one you watch the birds eat.
Picking
A ripe mulberry is almost black, not red, and falls into your hand. The classic method is a sheet spread underneath and a gentle shake, which gets you a bowl in a minute and leaves the unripe fruit on the tree for next week.
They do not keep. A day in the fridge, or straight into the freezer, and that is honestly the right answer: a bag of frozen mulberries is the best thing you will get out of the tree.