Welcome to Just Answer. I will do my best to fully answer your question(s).
Your leak may be something as simple as one of the drain piece connectors dripping or it may be coming from where the faucet and /or strainers connect to the sink. Based on what you told me about your no to old disposal it likely is not that.
I am not familiar with prices in Atlanta but likely a $100 minimum if it includes a travel charge which most do these days. As for a recommendation, we arent allowed to do that on the site here sorry.