A few things...
Winchester doesn't make anything but 12 Gauge guns at this point. IMO "all the help you can get" doesn't mean using a fancier, more expensive version of bubba's duck gun to hunt chukar in the mountains.
4 shells is plenty; many states. e.g. Oregon, limit you to 3 anyway.
The 20 Gauge 391 is an absolutely wonderful shotgun. The only bummer is that it's walnut-only. I've seen one that's been used for a lot of chukar. The stock has been broken into two pieces, then fixed.
I found a rare 20 Gauge "Walmart 390" at Cabela's, NIB. It's a matte/synthetic 390, more suitable for rough use without cringing. I don't think the 20 Gauge 390 is made any more. I'm looking forward to using it for chukar this year.
The 3901 is ostensibly available in 20 with a synthetic stock, but I haven't actually been able to find one.
26" is a perfect match for the Beretta 20 Gauge, IMO.
If you do go for the Urika 2, which again I think is a wonderful gun, and you have a Cabela's near you, check out the Ultralight version they have (it's on sale, and I think only Cabela's has it -- the 20 is around 5.9 lbs. like the pricey Teknys, but the price is like the regular Urika).