Too add to the more realistic aspect, older people are probably more likely to need and to want a fitness program. Looking into older adults needs might very well help too. And at times need a bit more special needs because of compromised health situations.
As far as picking and choosing who you want, that is fine, as long as you understand you may limit your income potential a bit that way.
I am guessing the people who will be your clients will most likely be the ones who can afford a trainer, week after week after month after month.
Also, one of things we learned at ACE, (I took the course but let me say, I never went on to be a paid full time trainer) was "keeping" clients longer term. Keeping their motivation especially, goals and interests in sight and keeping things interesting. I think it also pays to be a pretty good listener (for some), since some people just need someone to pay attention to them and listen to their problems at times.
I also do not think one has to be limited to the gym, as I knew our teacher/trainer played tennis, basketball, jogged a track etc. with clients.
As you gain more experience, who knows NFL/NBA/MLB pro athletes etc. aim high!?!?