I run in the same shoes I use on the street. Asics Nimbus. That's the top of th eline Asics shoe for a neutral step. Neutral step means my feet don't roll in or out, my shoes wear evenly. There are other Asics shoes for people who roll their feet either direction, I don't know the names. You can determine what shoe you need by looking at the wear pattern on an older pair of shoes.
Finally, the Nimbus are quite heavily cushioned. They have the most amount of gel in the heals to suck up the most shock and rebound on concrete. If you're going to be only on a treadmill you won't experience as much shock and can use a lower end running shoe. It will ultimately be cheaper, and they'll be lighter too.
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