Well early in game I have 3 fleets of 4 small cutters. This will usually keep the ai off my back until I get Medium. 

Medium ships are my backbone fleet. I make Assault craft and Escorts and Guardians all are medium. All get 2 engines and 2 thrusters and various mix of weapons based on resources or where I want to build them. 

Large ships are where I usually stop at and almost never need to go up to HUGE. Large ships have 3 flavors, Heavy Capital attack with 80% weapons 20% defenses, Command ship which is all Fleet enhancing, resource requiring modules. Sometimes Ill arm them but in most cases ill just add another carrier module. and finally Carriers. These get nothing but 2 engines and usually 3 carrier modules. 

I found that the best fleet is one that has escorts and Assault ships with capitals and a carrier and a command ship. Guardians are really not needed so far. 

+2 coppers. 

I never  build tiny ships. I always get to small and start there. After I get medium I never build small unless I need to garrison a military starbase. 

I only use smaller ships for two reasons (both production-cost related):

1.) Late game I have a small-size sensor ship following my bigger ships around, decked out in crappy engines and life support.  The stock life support only costs 4 production and the hyperdrive plus is something like 10, so you can get some really cheap ships with decent speed and range plus 12 sensor range.  I do similar things with troop transports (which currently only require 1 troop module to take planets) and short-range constructors.

2.) Basic defense ships.  Crappy shipyards can at least pump out planetary defenders that are small-sized (or tiny, but those can't fit defense) and they'll beat low-tech warships and prevent transports from landing on your planets.  My current game I also needed way too many ships way too fast so I pumped a bunch out, although if I have time or it's late enough that I'm mass-producing medium and large ships then I'll skip the small size since they can't carry nearly as many engines and life support as larger ships without sacrificing their firepower or defense.