I've had permits issued by Etowah, Shelby, & Jefferson.
I'm originally from Etowah County so that was my first. The process was simple, cheap, and relatively quick (I think it was 3 days). That has been YEARS ago though so I don't know what it's like now. My guess is that it's still not a problem.
Shelby County is the most expensive but is also the fastest and easiest. Walk in with your money and info, you get run through the computer, and you walk out with your permit.
Jefferson is not a problem, but I ALWAYS go to the Bessemer office. It's less busy and they people are always friendly to me. I think the form says it can take 3 weeks, but mine was ready the same day. They do require 3 references and 6 months residence.
Tuscaloosa is AFAIK, the worst of the lot. One of my buddies is in his 40's and served in the Army and Coast Guard. But because he decided to go back to school and is a student, he had to go and apply to the Sheriff's office AND the campus police. It's a screwy setup where one won't approve it until the other will and they seem to take their own sweet time.