The down side of a 20 gauge is the more limited selection of defense ammo and the usually higher cost.
If you select effective 20 gauge defense ammo the recoil will usually be the same as reduced recoil 12 gauge, and less shot in the air.
It's generally not recommended to leave a pump gun cocked due to concerns about both safety and wearing of the hammer spring.
One of the safety concerns is if there was a fire in your house the chambered round would fire, endangering you and firemen.
Many people do keep a round chambered, but most leave the gun in police "Cruiser ready" condition..... Magazine loaded, action uncocked.
The gun is perfectly safe and all that's needed to use it is to pump the action.
As for defense ammo, most experts and police recommend a buckshot.
The most popular are #00, #4, and #1, with #1 buckshot being considered the perfect load because it penetrates better then #4 and gives more hits and damage on target then the larger #00.
Slugs are used by some people, but a slug turns a shotgun into a modern musket that requires more precise sighting then a shotgun loaded with buckshot, and increases the chances of over penetrating.
Inside the average house it's easy to just plain miss even with buckshot, and very easy to miss with a slug.
These days for a true home defense shotgun the reduced recoil ammo is gaining popularity due to the lower recoil, which allows faster follow up or multiple target hits.
Many police departments are going to reduced recoil because of smaller men and women cops, and to encourage use of the shotgun by not pounding the user too badly.
Another mistake often made is over-accessorizing a shotgun. Everything that's added to the gun has a price, and that's weight, bulk, and slower in action.
The great advantage of the shotgun other then the devastating load of shot is the speed at which you can get hits on target.
Virtually anything you add to a shotgun will slow down that speed of hits.
You have to do a Real World cost-benefit analysis of each addition to determine if whatever actual advantage it adds is not outweighed by the reduced speed of which it can be brought into use.
One critical failure to be watched for is not so much weakened magazine springs, it's shotshell compression.
If a shotgun magazine is left loaded there's a chance the spring tension will cause the shells to start to collapse and begin to bulge in the middle.
Inspect the ammo in the gun at least once a month and if you see any bulges shoot it in practice and reload with fresh ammo.
I once had an 18 inch barrel Remington 870 Police with the factory magazine extension that caused some Federal #1 buckshot shells to develop bulges in one month.
The ammo most prone to bulging is foreign made ammo, and cheap ammo.