'Value priced' shells do vary in quality. The worst shells in my experience are the mentioned Winchester 'High Speed' and one called Diana. Crapola.
Federal makes no poor quality shells. Their Top Gun is very high quality, as are the Federal shells sold at (gasp) Walmart. Of course, with the latter you have a choice of 3 Dram or 3 Dram. It's a great trap load if you can handle it.
Winchester AA is still good quality, although I avoid anything else with that brand name on it. The mighty have truely fallen, although their AAHS in 410 is the best 410 available in my humble opinion.
Remington is the best of the best. STS is still compression formed in 12 and 20 anyway. Best reloadable shell in those two gauges and the Gun Club is a good econo load.
RIO is loaded in the US now, and is top quality all the way although they use a hull which is poor for reloading. For a throw away, I recommend RIO all the way. Fine product.
Fiocchi is also most excellent, probably the best 16ga shells available.
Reload if you wish or have to, but right now new shells are priced the same or less than the components if the factory loads are useful to you.
Rem, Win, and Fed all have current rebates on target loads.
The market is a solid 'Buy' right now.
