I usually have three to four main attack fleets. Generally, each ship type of a certain size gets a name and keeps it, and I reflect retrofit Versions with a new class name. Here's the example: All my plain-vanilla attack ships for the Droyne Empire of battle cruiser size are named Rue. In one fleet, they'll be named: Rue 1, Rue 2, etc. In the second, they'll go Rue X, Rue XI .... In the third: Rue A, Rue B .... Helps me keep track of which ships are in which fleets in the massive ship listing window. Each ship keeps its specific name, and the class name will update with a small letter as it progresses. e.g.: The first-generation Rue battle cruisers are of the Rue class, the next generation are Rue-a, the next update is of class Rue-b, etc. If I can't update them easily, I don't keep too many obsolete ships around -- mostly 'cause they're deep in enemy territory, harassing until they're beyond repair.
Typical fleet design is one (maybe 2) dedicated fleet tender (repair and supply only), 4-8 attack ships, a sensor ship/mine sweeper and, depending on the race or game phase, a spaceyard ship, a ship capturer and/or a planetary assault lander. Balanced fleets with specialized ships seem to work well for me. Battle cruiser is my favorite size -- lots of space, but you can still max out on engines to keep the fleet fast.