Salam sis,
Congrats for reverting mashaAllah. I'm from Birmingham too, but miles away from you. I think the Green Lane mosque is good but perhaps The Central Mosque on Belgrave rd, near the City Centre would be easier to get to. It's near Five Ways and I'm sure there are sisters there who will be more than willing to help.
There are some good Islamic Book shops on the Coventry Road, Small Heath.
Amsons, The House of Knowledge and there's another one which I can't remember the name of. But they are all close to each other. If you stoll along the Coventry Road, (City Centre side), you will find them easily. You can get some good books from there inshaAllah.
But do check out the links Fi bro gave. I hope that helps. Best of luck.