The recommended limit for PADI-certified Basic Open Water diver is 60 feet beneath surface of the water. An Advanced Open Water diver may descend to 130 feet. Technically trained divers in good physical condition using gas mixtures (helium-oxygen-nitrogen) may descend much lower than that. I suppose my response depends on what you mean by "deep sea diving".
I will tell you that scuba diving has been very good to me, and I've been doing it for years. It's an opportunity to discover and appreciate what others cannot witness, even in well-stocked aquariums. Today's equipment and instrumentation permits you to dive comfortably while controlling and monitoring all aspects that a diver depends upon for a safe dive. I invite you to discuss your interest with dive shops near you. When you find an instructor with whom you can communicate well, you may want to look into training, which usually consists of classes, practice in swimming pools, and certification dives in open water.