from what the big shots say (Cressey, Boyle, Robertson, Dos Remedios, Cosgrove etc) it doesn't rally matter. ACSM, ACE, ISSA, IFPA, NASM, NSCA and some others are all good. Of course most of the big shot strength and power trainers seem to be NSCA certified. Boyle and others believe in internships and learning as much as you could after getting certified.
Understand that most full time trainers don't work with "relatively fit people" and I have found out that runners often have a lot of dysfunction, imbalances, and weaknesses. With that in mind I went the NASM route as their starting point suggests this and I like their corrective exercise specialty. It is pretty dogmatic but well respected.
Some of the certifications require you to go to weekend clinics and some you can do on line. They all require continuing eduction which is a good thing but some of the certifications are costly. The book Becoming A Certified Personal Trainer by Robert Wolff is a decent resource, find it in a book store, read it there.