If its for general target shooting you want to get a 1oz or 7/8ths slug thats going about 1300fps. Thats going to be like the challenger stuff, fiocchi, S&B ect. Usually marketed as low recoil / tactical.
For hunting usually its a 1oz slug going 1600 fps. Winchester or Remington are decent. Costs more and kicks more and usually only sold in boxes of 5 at a time.
590 Barrels are smooth bore so there's only so much you can do without a rifled barrel and sabot slugs. The groups you listed sound pretty much on par for what can be expected.