I'm another South Manchester resident, been here on and off since 1993, been here permanently since 1999.I freaking love it here, personally, big fan of Chorlton. Love it. Its a suburb of the city with a village feel. Other parts of South Manchester are nice too...
Like Lindyloo said, there are areas to avoid, there are areas with bad reputations but they are actually not as bad as one would think and they are lovely places to live (Whalley Range in particular, not a good reputation (thanks to Morrissey) but its a lovely place to live with nice parks and good schools. I don't know how much rentals are, but Chorlton, Didsbury, Fallowfield (ignore the triple murder there on Sunday...its a nice area) are all very close to the city centre. Avoid Moss Side and Hulme like the plague. But the other areas I mentioned are nice family-centric places.
There is a lot of crime in the UK, there is a lot more house burglaries than in the states, but if you are smart and take good security precautions (you know, panic room, snipers etc) you will be absolutely fine. Its a fantastic city and a great place to live.
I think one thing about South Manchester that would appeal to people from outside of the area, is that SM is full of students, university staff, and transplants, so its quite easy to be an outsider there, they are used to them. When you go to other areas (for example, gingajoy...Bury) its very insular and there are a great deal of ethnic minority groups which while exciting and diverse, do not go outside of these groups (I base this on the fact that I do recruitment for a major UK company and this is what we find in our Bury location) Bury is also not that close to the city centre, although accessible by Tram...
This is just my opinion..