I studied in Austin, and visited the city often growing up as my grandmother lives there - you're lucky to be moving there, it's an incredible city. Because there is such a gigantic public university there, along with several smaller colleges, most of the downtown/near-campus apartment complexes are overrun with noisy students.
For a family living in the city short term, I would recommend looking in the north/northwest areas of the city. For example, my grandmother lives off of Loop 1/MoPac near Far West Blvd., and it's a great area with convenient grocery shopping and good schools. My ex-boyfriend's aunt used to be a professor at the university, she and her family lived in this area as well and had only good things to say about the elementary school. There is also access to the shuttle system, which is good for getting downtown if you don't want to drive.
As for getting a car, there are about a million dealerships around, but I would also recommend checking out Craigslist because a lot of people use it in Austin, and I've heard of several people who happily got a great deal on a car through the site.
I can't think of anything else at the moment, but I hope this helps at least a little. Best of luck with your move, and say hello to Austin for me, I miss it!
