I haven't really exercised for quite a few years now and I'd like to get back on the bandwagon this year starting with some treadmill running (along with some other gym based things like ellipticals and bikes)
What type of running shoes would be good for an amateur runner with extremely flat feet? What types of things should I be considering when looking for shoes?
I don't think there's any particular shoe you'd need, but a couple of things you won't need:
Other than that, any running shoe that works for you in general would be fine.
A running shoe is a running shoe, but find the one that fits to your foot and your stride correctly. The assumption is the way you run on a treadmill will be the same as inside. Go to a store and try a few on and run around a bit in them, even if it looks a bit silly, just find the one that you feel wont cause injury.
Just to add to Eric's answer the two most important things I look for in a running shoe - I am all treadmill due to nasty shin issues I get running on hard surfaces - are:
light weight
cushioning
Stability, how well the shoe is made (toe/heel forms), and all the extra stuff is really nothing to worry about since you aren't cutting, your shoes are scuffing, you aren't hitting potholes, and such. So I have been buying some running shoes lately that I would have never bought before if I were running outdoors as a lot of the new ones especially from Nike and Adidas have virtually no ankle support.
