If you want to leave from LGA, there isn't any major presence of any one airline.
At JFK however, there is American, TWA, Delta, and a little United, plus a low fare airline called Tower Air that flies all 747-400. (not exactly low-fare plane)
If you want to fly out of Newark and you want the most non-stops, you best option is Continental, as they operate their most profitable and second-busiest hub there. There is also a semi-strong presence of American and United, and some Delta.
If for some reason you are more concerned with FF programs than most non-stops and convenience, United and American are the main carriers of Star and oneworld, respectively, Delta partnered with United and most recently Air France, and Continental is partnered with Northwest, Virgin, Qantas, and others.
Since you will be flying a lot, the best elite level program is from Continental (they won the 1998 Freddie) due to unlimited free upgrades for even the lowest tier.
Personally, I would go with the airline that has the most convenient schedule with the most non-stops to the cities that you will be frequenting and then worry about the rewards later.