There really is not one OPTIMAL way to build fleets in Aurora... Even if I play in a campaign with nothing but AI as my opponent I always build my fleet as if I could face an opponent that would tailor their ship design against mine and/or change their designs over time. I often also play multi-faction games and in those I often have to compromise designs so I have a fleet operational at a decent cost for said faction to defend themselves and what colonies they possess.
I would never go super specialised on anything bigger than below 10k in size, in my opinion that is not militarily sound in all but a few instances. Every ship obviously should have a primary role which can be something like Escort, Patrol, Scout, Carrier etc.. What I have learned from most multi-faction campaign that I have run is that having too many very specialised ships make you vulnerable to them being singled out and that quickly lead to a disaster. You are better of having some primary beam weapon on all major combat ship as an example. If you expect to ever be fighting at close range then ships with no beam weapons can just be ignored and that is allot of defensive armour and hull that can do nothing but sit and watch while your only beam ships take all the opposing sides incoming weapon fire. The same is true for any specialist role you build. The AI might not be smart enough (but can do it by misstake) to exploit that but a real opponent would. It is up to you how much you care about that though.
There is no problem having a few specialist purpose ships but a fleet still need to have decent coverage on all their ships so one ability can't just be knocked out in a single blow with minimal effort. If you have an "escort" class destroyer then make them primarily for engaging enemy missiles with some PD and AMM and at least one primary beam weapon for self defence and a basic resolution 1 sensor for medium distance missile defence.
Use lot's of smaller sensor scouts as they are may more efficient for long range scouting than large vulnerable ships. Don't go around broadcasting your main combat ships positions with active sensors, use really small scout craft for doing that and/or small dedicated reconnaissance frigattes (2-4kt size)... in general resolution 80-120 are generally considered main active sensors so anything below 4kt can generally go undetected relatively easy from such sensors at decent distances in the early game.
Don't settle for any specific size of ships and really don't fixate about the naming conventions too much. I generally use the naming as substitute for role and to some extent size, but mainly role. There is not much reason to have two different escort ships of different sized just so you can call one a frigate and the other a destroyer escort if they both are pretty much identical except for size, that does not make any real sense, at least to me.
In general an early Frigate might be 8000t while fifty year later you build the ships of the same role at 16kt, at that point the old Frigate are either completely obsolete or you simple change their role to something different, perhaps a system patrol craft or something.
Generally larger ships are way more efficient than smaller ships but smaller ships are faster to build so there is a fine line between how long can you wait until those really large ships are built and ready for combat versus allot of smaller ships you can have earlier but over time will be weaker. A large ship generally also have more complicated and expensive components from a research perspective which also have to be factored in. But overall, the larger the ship the more effective it is in using mission tonnage... but certainly not in terms of stealth.
In terms of size you could ask yourself, if I always need five 10kt ships to do something I might as well just build a 50kt ship to do the same thing but just do it better. More ships just means you are more versatile on the amount you can operate in more places at the same time, sometimes two 10kt ships is enough then it is a waste to send a 50kt ship. Two 10kt ships also project a much smaller thermal imprint in space so are more stealthy if that is important.
Over time it is cheaper from a maintenance perspective to have really large main combat ships supported by smaller more specialised ships, you just need to find the magic balance of the amount of which you need and there is no good answer for that. But in general, the smaller the ship the more specialised their role generally tend to become. Use as few ships as possible to accomplish your missions, bigger is generally better than more.
In terms of weapons and defensive system I think that most have been said about that, start small and select one or two primary weapons system and expand on it later on as you establish yourself economically. Make sure to keep research focused on expanding your economy but don't neglect pure military technology either. Focus primarily on a defensive fleet and defending your colonies before you contemplate going on the offensive... focusing on a strong economy first will generally just make your fleet grow even stronger over time, but don't neglect your defences and spending.
I might not really have given you any hard fact on what to do but rather how to think about what you do instead and I hope it has been to some help.