The metro-train to New Street is frequent and fast on the line that runs through Edgbaston. It takes about 25-30 minutes to commute from Sutton Coldfield/Four Oaks and that's quite far out from the centre.- I would look for anywhere close to any of the stations on that line.
As Raymond said 45 mins is a long way on the train so you could live in a huge radius, personally I would avoid the areas immediately adjacent to the centre, including Edgbaston, but it all depends on your budget.
I rent out Four Oaks and it aint cheap at all.