To give up his parental rights and obligations prior to my having the procedure. What's the most cost effective way to do this in Georgia

Get a written agreement drawn up and noterized .
As far as I know that should cover it,
But it may be worth having an attorney look it over.

Notarization only verifies that the identity of the signators have been verified. You NEED an attorney to draw up an agreement that will comply with the law and provide you with protection in case the sperm donor changes his mind.

To give up his parental rights and obligations prior to my having the procedure. What's the most cost effective way to do this in Georgia

If you want a donor not to have rights you must use sperm bank.
Four states supreme courts ruled that the known donor has all rights and responsibilities.
Even if he signs relinquishment of rights it will be null and void. Thus he will be able to open a case for custody and visitation at anytime.

Many states treat contracts dealing with surrogacy or the relinquishing of parental rights as "against public policy," and render them unenforceable. Even if you and the father of the child have a carefully written contract that says he will not have to pay any child support or that he gives up all your visitation rights, courts may very well throw out the contract in court, and can force full parental obligations on him.

Agreed, you will still be having his child, and he will have the risk of having to pay child support till the child is grown, and you would have the risk of him wanting partial custody or at least visits also

The bottom line here is you can't give up something you don't have in the first place. Also making a contract doesn't mean anything if it contains illegal language in it. It must be enforcable by a court of law. That's why its recommended you find a lawyer and a sperm bank to handle the problems legally.