Slug gun accuracy is a very strange thing. One twist rate is no more accurate than another. One barrel length is no more accurate than another. The scientific theory is that the faster rate of twist helps stabilize the faster slugs. I have found it to be true with my own experiences and yet I have read where other people with the exact same setup that I have, having the opposite results. My 870 with hastings barrel (1:34 twist) loves 1oz slugs traveling at around 1500fps and hates faster, lighter slugs like the hornady slugs. I have read where others with an 870 and hastings barrel love the hornady slugs. My barrel is pinned, maybe thats the diference. I think what plays the greatest role is how well your gun fits together. The looser it is, the more vibrations and the less accurate it is. Thats why fixed barrel shotguns like the USH as well as the bolt shotguns like the savage 210 are usually more accurate than shotguns with interchangeable barrels like the 870. The USH's are suppose to be about the most accurate you can get but at the same time, you will hear of people that can't hit anything with them. I think thats probably because there was some factory deffect where the gun did not fit properly together.
Your best bet is to just get something that you like and then buy a bunch of different weights and speeds of slugs and figure out what works best in your gun.
20 gauges always have a faster twist rate than 12 gauges because of slug weight and speed. The 20ga is suppose to be more accurate than the 12 ga.