I was in much the same situation as you are a few years ago. I flew, at most 25K miles per year and had no single airline that I concentrated my flying on. I was able to build up fairly sizable balances on Northwest, Delta and United. My Northwest and Delta accounts were merged after the takeover, so I now have more miles with Delta than with my current preferred airline, United.
Given that you may barely qualify for the lowest level of elite status with one airline if you concentrated on one airline, you might be tempted to stick with only one airline. If you usually travel "heavy" with more than carry-on baggage this can save you checked luggage fees which can be substantial. This would probably be your primary benefit flying out of NYC because as the lowest level elite, your chances of an upgrade out of NYC can be very slim given the high number of high status flyers in the Big Apple. For example, I am a 1P with United which is mid range status, and I don't rate at all out of NYC.
If you must have nonstop flights out of NYC to FLL then your best bet is probably Delta, unless you can fly out of Newark, then Continental would work for you. Also if you fly to Germany a lot then you would probably want to be hooked up with *A (Star Alliance) because of their tie in with Lufthansa which has lots of flights to Frankfurt and easy connections to the rest of Europe.
Basically, you probably would want to concentrate your flying with one "alliance" and try to get and maintain at least the lowest level of status with that airline/alliance. If you can handle Newark every once in a while, then stick with Star Alliance and choose Continental (for your nonstop FLL flights) as your FF program of choice. You can credit flights on all Star Alliance carriers to your Continental FF number, including United (some transcons to SFO ad LAX if you ever go that way), US Air (LGA mostly) and Lufthansa (good flight schedule to Europe). That should cover most of your flying needs. Just be sure to credit all of your flights to one program.
Read up on the various alliances and see which one fits best for you. American Airlines is also a possibility if you can fly into Miami. I don't fly into Miami anymore unless I can't help it. FLL is too nice on an airport to pass up.