The best way to store an automatic watch you're not wearing is simply flat or on its side, out of direct sunlight, somewhere it won't get knocked around. You don't need a winder for a watch you'll wear again within a week or two. You only need one if you want it running and ready to go the moment you pick it up, and even then it's a convenience rather than a requirement.
A watch box does more than a winder for most people
If you rotate between a few watches and don't mind resetting the time and date when you switch, a simple watch box or even a soft pouch is all you need. Automatic movements are designed to stop and start again without any harm, so letting one wind down for a week does nothing bad to the mechanism. Store it away from magnets, heat vents, and windowsills, since both temperature swings and magnetic fields are more damaging over time than simply sitting still.
Keep the watch in a stable spot with even humidity if you can. A closed drawer or a padded box on a dresser works better than a bathroom shelf, where steam and temperature swings happen daily. If the watch has a leather strap, storing it lying flat rather than coiled tightly helps the leather keep its shape over long stretches of not being worn.
When a watch winder actually makes sense
Winders earn their keep for watches with a perpetual calendar or a complicated date function that's a genuine hassle to reset, or if you simply like grabbing a watch and having it already keeping time. Set the winder to the manufacturer's recommended turns per day rather than guessing, since over-winding an automatic on a winder can add unnecessary wear over months of constant motion.
Skip the winder for everyday pieces like a Seiko 5, since resetting the date takes seconds and the movement doesn't benefit from running nonstop. A winder is a nice-to-have for a serious collection, not a requirement for keeping a good watch healthy while it rests.