There are three teams in the Birmingham area that I know of - one runs an air-cooled Beetle out of Hueytown, we (Half-Fast Racing) run a New Beetle out of Alabaster, and there is a Dodge Daytona team (Dodgie Racing) closer to downtown (I think). Frank Camper gave me some good advice on putting together a team and car as I was getting started last year. I'll be glad to pass his advice and my own "lessons learned" on. If you send me a pm with a phone number, I'll call this weekend.
I think the Dodge team is looking for drivers - check the forum for the post by "naking" a few days ago. Joining them for a few races would be a good way to learn a little about Lemons rules, racing, building and running a car, and running a team before actually hitting the track with a newly formed team. I drove with Orca a couple of times before we got our car together, and it helped a lot to not be learning everything at once. Plus your car build may take longer than you think.
I also did what DirtyDuc suggests - funded the car build but have drivers pay their own way (more or less). I'd be racing even if it was just my wife and I driving, so I don't worry too much about breaking even. Plus my other drivers are all friends and family members so I keep "driver cost share" fees lower than most teams but try to cover most expendables. Talk to several teams about costs. They will vary, but will add up fast; and it isn't just tires, gas, and brakes. "Budget racing" is a relative term.