If you go in person you get a copy then and there. Also, know that you can get it from ANY county clerk in the state.... though really tiny counties can't do it immediately, most can. I got one for ds in wichita county (wichita falls) after an airline gave me crap for flying without one and i got it while visiting family.
Re: Birth Certificate
I mailed in a form that they gave me at the hospital-- didn't have to go anywhere to get it.
If u have that to mail in, just know that they don't take checks! They sent mine back even though nowhere on the form said no checks...
Took about 3 weeks after i re-sent it in with a money order to get it..