I like the stock TMP fighter. It's a nice and imaginative effort to present fighters in a universe dominated by capital ships. Certainly more convincing than the later examples presented by canon TNG, anyway.
Likewise, Thu11s presents a 'heavy fighter' that comes across well as a bomber.
As to organization, it's your choice as you're the skinner. However, when considering it myself? I'd look at how the US navy is organized and use it as a basis. Certainly a Marine force would have access to their own fighter vessels (and their own specialized space-navy craft, as the US navy has presently) but when it came to space battles, most operations would be performed by pure navy craft. One doesn't ask the marines to participate in ship-to-ship combat, do they? (outside of boarding actions I mean).
However, it does raise the question of how space navy and marine fighters would be configured for their missions. I'm not sure if SFC:OP accepts new fighter classes easily (whenever I've modded fighters, it's usually been a disaster), but if they can, perhaps a modder should consider separate variants of federation fighters for navy, marine, and army use.