Most certification agencies offer decent training for simple open water diving. The important part is how you implement that training under water.
SDI, TDI and ERDI are associated with each other, with SDI geared toward the casual diver, TDI the technical diver and ERDI Public Safety diver (those intrepid folks who pull bodies out of sunken cars, search lake beds or perform fast water rescues).
PADI is the leading certification agency in the US, but not worldwide. They have great marketing and decent training. After training, their purpose is to sell you more training.
NAUI has been around longer than most and was the original certifying agency, typically working with the YMCA many years ago. Early NAUI instructors came from the Navy. One NAUI course is worth 3-4 other certification courses.
There is also SSI, which provides training in the US. It seems to be a popular alternative for recreational divers.
No matter who you choose for training, remember and implement what you were taught and don't dive beyond your limits. And when you are out there in the ocean, don't blindly follow your dive guide, regardless of the number of certifications they claim to have. You are responsible for using common sense and enjoying the next dive.
Finally, if you are venturing out of the US, be sure to have dive insurance. You can get it from DAN and a few other companies.
-Rob