A bit late to the party, but this is one of my fav subjects.
In general, the size of my ships is more based on tech level and my industry base, and the designations are based on role, slightly influenced by RP. The more pompous I imagine a faction I'm playing, the more likely my first ships are to be cruisers, rather than destroyers. Also typically if a ship I make has independent sensor capacity, it gets upgraded to a cruiser, even if it's technically a destroyer. I'd lump them in with light cruisers, in addition to the role for CLs I mention below.
An early fleet (not counting support elements) for me typically consists of only two types of ships, one for AM defense and emergency FAC/fighter defense (for a certain spoiler race... turns out it works really well to use AM laser turrets against the little buggers). The specifics of how I name them depend on the flavor of the story, but typically I stray away from using the escort designation for some reason, especially odd as I interchange destroyer/cruiser as RP demands. Sometimes I will add a missile designation on cruisers as the fleet expands and I put heavy missile emphasis on one class. Destroyers with missiles don't get special treatment though, and I reserve battleship and the like for beam ships, so this can result in a missile cruisers being considered the pinnacle of my fleet development if I go the missile route. In fact, I tend to avoid using designations of anything heavier than a cruiser, save a carrier, witch is a special case. In the event I need something heavier than my mainline, it's a battlecruiser, not a battleship.
Anywho, with that preface, here's what I use, in order that they typically appear.
DD - Destroyer (Focus on defense using beams)
CC - Command Cruiser (Main sensor ships/flag bridge/etc)
CA - Cruiser (Offensive Ships)
CG - Missile Cruiser (Optional name for missile armed offense as tech level increases)
CL - Light Cruiser (Scouts, and may have them carry one scout fighter or "float plane" as I would call it in naval terms)
BC - Battlecruiser (Heavy Cruiser basically, beam armed)
CV - Carrier (Self Explanatory)
PC - Patrol Craft (Typically missile armed FACs for quick hit and runs. I've been known to experiment with loading them into carriers too)