SDI is somewhat new and not a ton of places I know do the course. I don't know anyone who was certified by them so can't talk about the program. PADI is the most popular and has shops worldwide. When I got certified as a kid it was through the National Association of Scuba Diving Schools (NASDS). Now defunct. Got re-certified with PADI because I didn't dive for a while. Also when it was time for DD to learn to dive, it was with a PADI dive shop.
The big thing is to pick a place where you trust the dive operations and instructors. A good instructor makes a lot of difference. I was happy with the PADI curriculum and the instructor that taught Andriana.
The problem with PADI (and maybe SDI, I don't know) is that you are certified after pool dives and 4 open water dives. A good start but you should have some guided dives after certification for the experience. Some people think that once you get the card, you are Jaques Cousteau. After A had a few dives under her belt, we both took the Advanced Open Water (AOW) Course together. AOW teaches advanced navigation and a other good courses. You can also get Nitrox certified. They also have more advanced courses including Tech Diving. She may go for her Rescue Diver Certification this summer.
It is a great sport and whatever you decide, I say go for it. Since I got her certified, we had great father/daughter trips and many adventures. Not many kids have photographs like this. Of course we had to go to Hawaii to get that.
If you want to travel down here, I know some great instructors. It can be done in a weekend wherever you go. Glad to answer any other questions you have,