I did this last summer and the rail fare was about 30 pounds (~$US45) return ticket. I think I recall I travelled on a Friday, and you could do better (20 pounds) if you were flexible. There is a UK integrated railway website that can do quotes and lets you purchase tickets:
www.TheTrainLine.com
Nice thing about BHX is the mainline railway station. Nasty thing is the bus connection between airport and station - there used to be one of the few operational magnetic levitation trains in the world connecting them, but it isn't operational anymore.
BTW the BA Terrace lounge in Birmingham is one of the nicest lounges I've been in and away from peak am and pm flight times is pretty quiet.