First and foremost, welcome to the forum and congrats on your new Mossberg.
There is not just one way to keep a shotgun ready, however; if you have multiple shotguns or rifles you should use the same methodology across all of them to avoid confusion and a possible unintended discharge. The other consideration is if you have kids or other adults who have access to the the gun. Safety first!
The method you described with a round chambered and the safety on is perfectly acceptable. The potential drawbacks include something or someone inadvertently hitting the safety to the on position, thus making the gun ready to fire. And while the Mossberg 590 is "considered" to be drop safe many shotguns are not, even with the safety on, and I'm not sure I'd trust any of them.
The method many of us use is to take a completely unloaded gun and rack the slide action and then pull the trigger to dry fire the gun. At this point you have a completely safe gun and it's your choice if you engage the tang safety or not. Many folks, using this method, do not engage the safety. Now you can load the magazine with your choice of rounds. The condition of the gun is now known as cruiser ready.
To bring the gun into action you simply rack the first shell into the chamber and the gun is ready to fire. Given you've first dry fired the gun on an empty chamber there is no need to utilize the slide release. This is considered by most as the safest way to store a loaded shotgun and have it immediately ready for engagement.
Hopefully this is clear but you should practice whichever method you plan to use outdoors in a safe environment. Plus using inert snap caps is a good way to practice loading and utilizing your gun. But safety first!