I tend to have four major fleets (if possible) (the names here are descriptive of the roles - in game names are often quite different)
Home Fleet - Strategic reserve & guarding the capital.
Expeditionary Fleet - visiting the Aliens and instructing them in the finer points of civilization and Fusion Cooking.
Transit Fleet - usually either on the way out to relieve the Expeditionary Fleet with newer/refitted ships, or on the way back with ships to be refitted/repaired, or in the home system being refitted/repaired. Frequently this becomes a Maneuvering Reserve.
Training Fleet - as it says, pretty much constantly in the home system on training maneuvers, also provides an Emergency Reserve in case I need to send Homefleet out to respond to some outsystem issue.
Fleets tend to transition through the first three types, Training tends to be a permanent fixture, with the individual ships rotating in when first built (or after a very big repair or refit that drops the training level) and rotate out again once they reach 100% (or sometimes earlier if I really need the capability NOW)