Cheap promo shells from any of the manufacturers have problems in "some" guns, not just from Winchester. Winchester Universal are the bottom of the barrel though, from the point of quality control.
Having said that, I have a wide selection of pumps, singles, over-under and side by side shotguns, newer and much older, and I have not had trouble with any cartridges of any type sticking in my gun's chambers. I do not own any semi-auto shotguns.
I would be watching for sale flyers for the lowest price at the time. You just passed the season where AA Winchester shells were on sale with a rebate from the manufacturer, making for a smoking good deal on quality cartridges. You can expect that a price between $7 a box and closer to $8 out the door buying target loads by the flat is as good as it gets these days.