Originally certified with YMCA, I also hold certifications at various levels with NAUI, PADI, NASDS, SSI, IANTD, and NSS-CDS.
In order of importance, you should look for:
1. A good instructor with whom you are comfortable. At your age you will likely be more comfortable with an older instructor (there are plenty - I'm still very actively teaching at 52 - almost 53) who's more likely to have tips & tricks up his sleeve to overcome common "age" problems (that we needn't discuss).
2. A good dive shop with which the instructor works. Having a place to go where they know you and every piece of diving equipment you own or use is way, way more valuable than the few bucks you may save "shopping around." A good shop will let you try gear before you buy, sponsor guided trips to great locations and generally provide any level of hand-holding you may want or need.
3. Agency. My personal preference for open water training is SSI, all other things being equal, but, as I and others have said, a good instructor is *the thing.*
Rick