Hi Blaisenguns,
Long time lurker. Your post made me join. I own a few 500's and 590's. I have been shooting them nearly 30 years (duck, dove, clays, paper). I am not an expert, but I have stayed at a Holiday Inn.
I would not invest in choke tubes for a dedicated home defense shotgun. If the gun is multipurpose - tubes are the way to go. Two sets of tubes that I have read about are Briley and Trulock.
http://www.briley.com/
http://www.trulockchokes.com/
Natman rightly indicated ammunition should be your first try. Pattern, pattern, pattern. You will find a wide variety of results from one gun. I used pattern area as the determinate. The smaller the area - the tighter the pattern. My first results from one shotgun yielded:
View attachment buck shot string 20060701.pdf
If I remember correctly, I shot five rounds each of eight different loads. Remember, a new target for each load. I did this on ruled flip chart paper (one inch grid). I "eyeballed" the results, so I have induced inaccuracy into the measurement (but consistently inaccurate). Likewise, I made mistakes in the exercise (different dates, sometimes mis-measured, different ranges, etc). In short -
do not use my results, but use my method. Plan better and you can avoid these. Also, consider - what is your maximum distance? Shoot at that distance. No real reason to pattern at 100 yards, if your maximum intended range is 12 yards. Be smart.
Also expect to walk. If you are limited to one target stand - 5 shots, 8 different brands, all 30 yards round trip for a new target between rounds - you get the picture. Likewise, remember the time - how does your range behave? Ten minutes between "trips down range"? Time can add up.
You may be able to achieve your goals through ammunition alone. For my dedicated shotguns, I worked with Hans Vang. He is an EXPERT. The results in the .pdf above are with a base 500 with a Vang ported barrel
https://www.vangcomp.com/Home.html
Please realize, you can put a lot more money into the shotgun, than what the shotgun originally cost. Also consider, if used in a actual home defense situation - the shotgun is likely gone forever. If returned, nobody will have taken time to clean it. Whatever goo and gunk was on it when it left, will have worked on it for the duration of its "vacation".
I have upgraded to the 590A1. I had Hans do his magic. I have patterned one shotgun with two brands, and another with one brand. Interesting to note, one shotgun patterns better than the other with the SAME ammo. Question - does the difference realistically matter at the range you have selected?
View attachment H13200 vs LE13200.pdf
I became more sophisticated in my measurements. I used On Target software for more accurate measurements. The software is great and easy to use. I got it for rifle work, but it works great for patterning.
http://ontargetshooting.com/tds/index.html
You can take a picture of your target, and get direct measurements off of it. NB - make sure your have a reference for size in the picture (I use a ruler). You can see different results in the attached two pictures. The results are CTC, group width and height, and others. Some matter for this (group width and height), some don't (CTC). Easy analysis of area in Excel (as seen above). Please note - these are standard IDPA targets. I did not "aim", but I did try to hit paper. Placement is not indicative, only pattern. Also remember, you do not need to go to 0.001 of an inch on a shotgun pattern. Likewise, you will see 9 shot shotshells loaded with only 8 shot....oh, well....
One modification I would do to any Mossberg is changing the safety. The safety is plastic and will break. Hans Vang has an aluminum one. Likewise, a pistol grip will defeat the advantage of the top mounted safety. You will have to "break grip" to work the safety. I prefer a regular butt stock.
I apologize for a lot of opinion and the length of this. I apologize for a series of error that I did in the different patterns, but you get the idea. Like anything on the 'net, take this with a grain of salt. I hope it helps.
Best,
Rabid