Support / Stability shoes are generally not the same as cushioned shoes. That's not to say they don't provide cushioning but the two qualities are somewhat exclusive.
From things you've said in the past, I suspect you'll need a support / stability shoe. As for specific recommendations, New Balance and Brooks are probably the industry leader for that type of shoe but all companies make a support shoe with good selling points. You really just have to go and try the shoe on (do that at a store even if you're buying online). Everyone's foot is different and we can't tell you what will work perfectly for you.