Here is a map showing the train route I mentioned above.
http://www.nationalrail.co.uk/css/NetworkRail_BirminghamWestMidlandsmap.pdf
Note that while many trains do come into New Street station there are trains that go into Moor St station and Snow Hill station that DONT go in to New St station so don't ignore them.
Both Moor St station and Snow Hill station are city centre stations and have less trains so a quieter so more pleasant to come in and out of if yo uare commuting.
On the map you can see the light green route that runs from Redditch in the bottom left up to Litchfield in the top right.
You can also see the orange "leg" that runs down to the bottom right into Olton, Solihull and Shirley.
Like most cities there are some pretty horrible inner city areas to avoid, but I wont list them here as I don't want to upset anyone.
btw The Jewellery Quarter is a good vibrant area for young people and there are quite a few new developments going on in the area. There is also a Jewellery Quarter station that takes you right into Snow Hill station and Moor St station (only a couple of stops).