Alabama is not the impoverished state it once was. Don't rely on old news and stereotypes to make your decisions. Do research instead. The job market in Alabama is very stable, and very healthy. Wages are decent, cost of living is far lower than most of the rest of the nation, and quality of life is actually quite high in most areas of the state. Yes, time are still tough for many people that live in Alabama, but for just as many, things have improved vastly, thanks in no small part to all the Asian automotive companies that have set up plant here, and all the industires that come with it. Many people in this state are making more money than ever before, and it is beginning to show in many areas of the state that were once bordering on vulgar poverty.
Yes, the school system does need work, but that is true nationwide, not just in Alabama nor the south in general. All American schools are far behind the rest of the world, whether you live here or New York.
Up front, Birmingham is a violent city. This years crime statistics speak the truth on that. Already over 70 murders so far in 2006, and still over 4 months left in the year. Birmingham is a perfect example of what happens to vibrant cities when people flock to the suburbs. Sprawl is ridiculous for such a relatively small city, but the center city is slowly making a comeback. There is nothing anymore unique about Birmingham in that area than any other US city that had its urban core virtually abandoned. Birmingham isn't great, but there are far worse places.
Overall, Birmimgham is a nice city with a horrible legacy it is trying to overcome, and if I may say so myself, it is doing a pretty good job of that, albeit slowly. Progress takes time, and Birmingham is no exception. It's full of history, charm and you won't be lacking anything to do, just study the city before you move, and find out about areas you are interested in. Some areas of the city are dangrous, many aren't. That holds true with any major US city. Do your homework.
As for culture shock, yes. You will have some. The south can be a very confusing place at first, it is for Americans that visit here for the first time, and it will be for you also. The key is, don't believe everything you have heard about us. It is no secret that Alabama has a very violent and inhumane past, but so does the United States. The people here are friendly, laid back, and generally willing to help, although admittedly a little wary of outsiders at first. Yes we do have rednecks, we do have trailer trash, we do have backwards thinking people, but show me what US state doesn't. You won't find one.
Enjoy Alabama if you move here. It's a beautiful state filled with great people, but it does have its problems. You just shouldn't let those problems overshadow everything that is good about Alabama. As for any predjudice against a British family, I don't think you will. Americans in general have great admiration for British people, and the UK in general. I highly doubt anyone is going to be anything more than curious about you and your family.
Remember, we used to be a colony.
