is read your owner's manual from cover to cover. Understand what instructions Remington is providing to YOU. You should follow those instructions to protect the functionality and preserve the safety of your firearm.
Semi automatic .22s are of the "blow back" design. This means they get dirty pretty quickly. Not only should you regularly clean the barrel, but you MUST make sure that any powder residue is kept from building up in the action area. Powder residue will accumulate on the bolt face, as well as any internal parts.
A .22 works on "proper headspacing". This means that the proper distance from the bolt face to the rear of the barrel must be maintained in order for the cartridge to properly seat itself in the chamber. Too much powder residue on the bolt face will increase the distance from the bolt face to the rear of the barrel, i.e. increasing the headspace. This can and will result in misfires, exploding rims, etc.
A .22 barrel will last for 100s of thousands of rounds. You do not need to do a complete cleaning of the barrel after each shooting session. Most of us target shooters only run a dry patch down the barrel every so often to remove excess bullet lube that accumulates. You DO have to clean your bolt face and action more frequently for the reasons I mentioned above. If you follow what Remington tells you in your manual, you 597 will last several lifetimes. A firearm is a tool. Treat it like one, and it should function reliably each and every time you use it. Good Luck with your new gun.