Bought mine (same gun) for the exact same reason. My wife has yet to try it. The 3/4 oz loads technically should not cycle the gun but I believe that the extra power (more powder) from the 1325 fps more than made up for the lower weight. The #6 is the size of the pellets in the shell. the higher the number the smaller the pellets. Two groups of shot shells bird and buck . The common bird shot ranges from #5 to #9, and the larger buck shot from OO (double ought) to #4. if the weights are the same, whether 1 oz, 7/8 oz or 3/4 oz, for a given shot size, the higher number = smaller pellets = more pellets in the shell = better chance of hitting target. there are some very good charts and explanations about shotshells on the internet. A good start is
http://www.shotgunworld.com/amm.html .
I have the same barrel. It is considered a tactical gun (and barrel) as opposed to a target or hunting barrel because of the shorter length and no chokes. That leads to the second item "cylinder bore" means the barrel has no chokes and the diameter is decided by the gauge of the gun (.410, 28, 20, 16 or 12 gauge). the higher the gauge, the smaller the barrel diameter. The shot will come out in a pattern as large as it can for the diameter of the barrel. Chokes narrow the spread and make the pellets hit in a smaller area (group). Google shotgun chokes to get some details.
Yours has no chokes as it is a tactical and home defense (HD) barrel and generally the wider the pattern the better.
In order to put a choke on your barrel, machining and threading would be necessary. The gun will work fine for Home Defense (HD) and practice just the way it is. One point however, using a slug for HD can have some drawbacks. You must be fairly accurate as it is a "bullet", a very big bullet with a lot of power, but it still only hits one point. The second drawback is that a slug will easily penetrate walls like wood, sheetrock, plaster, tile and I am not sure about cement block. A missed shot could easily end up in a neighbor's house even several houses away. third drawback, they have a lot more recoil than shotshells.
Most sources agree that shot shells are considered better for HD as they leave a little more room for error. NOT A LOT! at indoor distances of less than 10 - 20 feet, the shot from a cylinder bore barrel might only spread to 4 to 10 inches if that. Still easy to miss in a stress situation. It was recommended to me to use #1 buck shot. Even that can be hard to find. I opt for #2 buckshot in a 3 inch shell (more but smaller pellets). There is no such thing as the famed "OO buckshot" for a 20 gauge as it will not work well with the barrel diameter. The RIO #1 Buckshot is the biggest shot I have been able to find and not readily available. These "buckshot" shells have larger pellets about 1/4 inch and larger diameter and less pellets for the same weight. In the case of the #2 buckshot, 18 pellets in a 3 inch 1 oz. shell.
Lots of great info here and on the internet, just google it, but verify all information (especially mine) from several sources to confirm.
Good luck