I'm a newcomer, too, and I just want to share my perspective.
My hubby works for Regions Bank at the corporate HQ, so we knew we wanted to be south of the city. I explored many neighborhoods and small towns.
You are right, Chelsea is nice. It's a wee tad further out than you may need to go to get a nice lot, though. I have found very nice property between 459 and 119 (north-south) and 65 and 280 (west-east).
In Pelham, Helena & Alabaster, there are lots of choices, too, but visit the schools. Pelham high school has multiple mobile buildings in back, and that indicates strains from the fast growth in the area.
I also did a drive-by at Spain Park (very nice, new, well funded Hoover city school) & Hoover High (my first college was dwarfed by this behemoth). I considered Hoover High but heard that there was more gang activity there than in the other area schools -- granted I count this as hearsay, but I definitely find the Oak Mountain complaints of "they are always reminding you to tuck your shirt in" to be miniscule in comparison to "beware of gangs." Interestingly, I was unable to tour Spain Park when I was in town because it didn't fit into "their" scheduled tour dates. huh?
I visited Oak Mtn high school & was impressed - has a definitive county-school feel, which is good, but it is also large enough that I know my rising Junior twins will find the right social networks.
Word of warning to the wise: even if you rent for a while, look up property tax amounts. There can be quite a disparity within a few miles. The North Shelby area I mentioned has revealed reasonable property tax rates, but you may have other services and fees to pay out of pocket, and with lower property taxes, you may miss out on certain services that you are accustomed to receiving.
This is grain-of-salt territory, mind you
I hope you enjoy Birmingham -- I expect a great adventure myself.