You might be interested in the Alpha Centauri Institute.
We are a mature, quality fleet of role-players who conduct weekly and bi-weekly story lines, plots, and side-plots. We encourage all types of RP, and usually have several mini-plots and personal stories running at any given time. We attempt to run fleet action get togethers on at least a bi-weekly basis when time permits.
While the Institute is mostly themed as a Science division, we do have a military defense section as well. During in-game RP events, they are usually tasked with fleet protection and defense (when the situation demands it).
We are growing fast, and regularly have at least five to ten people online at any given time. If you'd like to see us in action, you can usually find some of us in the Lounge at Earthdock, Quark's at DS9, or Starbase 39. If you have any questions or would simply like to make contact with us, please contact either myself (Sanek@Cerebus06) or Silveda (Silveda@Quarie).
You can also find more information at our website: http://aci.guildportal.com. Our Recruiting page shows all the requirements to join us, and be sure to check out our forums - especially our Ten Forward board where we conduct our offline forum RP to get an idea of what we do, how we do it, and if it's right for you.
The ACI is a fantastic Fleet. I have run a few of their RP Episodes. Great people. Creative Stories. Tons of fun.
If you prefer something with a more Military feel. Check out the Sierra Defense Fleet. We are Allied with the ACI and other Fleets to make a pretty diverse RP Scene. There is a RP fleet that will fit just about any play style.