Well your fleet cap is dependent more on the number of spacestations you have and your population then on the techs. They add a total of 30% of my 350 or so.
The UNE just had its first war.... 24 years of brutal attrition warfare. But the aliens submitted to vassalization. What is interesting is when they were winning they would not accept a white peace...but somehow got offended when I kept turning down their offers once I got the war back in my direction. They have hyperlanes which meant fast fleet movement, which caught me off guard. Then they out teched me seriously...and so it was due to the sacrifice of several science ships I got some of their tech advantage via reverse engineering. I was using serious numbers of bases....Sol and Sirus are still plastered in bases. I lost several fortresses but the minefields cut him down...and just kept using my economic advantage to hammer out fleet after fleet.
Eventually had to emergency FTL out my surviving BBs in the last battle but by now I had taken over his home world and 3 others. My fleets were rebuilding and more to the point he could not keep killing my space stations and eventually the next time I went in with a 10K fleet he surrendered just before my troops started dropping.
One defence base stood off a missile fleet for months as its fighters and point defence kept killing everything they fired at it...and its return fire slowly but surely ate through the enemy force. I managed to force engagement in my favour a few times as well. But it was just a long brutal grinding match.
The war was over getting Terraforming liquid. In the end vassalizing the race didn't get me it directly but it allowed me access into a spiral arm area where some was. So now my terraforming efforts are going full bore.
I don't want to think about the cost of that war. I had 25K in minerals at the start of it and that got used up quickly. Probably 30K in fleet strength were lost on both sides if not more.
Just so you know...Corvettes can kill BBs and heavy ships as the heavy ships usually don't mount that many weapons that can shoot back at them. You need Small weapons from what I understand. The enemy force at the end was like 1 BB, 1 DD, and 50 CTs. I killed the heavy stuff and then I lost my CT/DD screen and should have pulled out as he still had 40-ish CTs. Had to emergency FTL away but 4 BBs survived that and well that was the last major fleet engagement he had at that point 26 CTs. That and the two other ones before it had broken his back basically.
Currently my "standard fleet" is: 2 BBs, 1 BB(CV), 4 CAs, 10 DDs, and 30 CTs. Mix of weapons: missiles, torpedoes, Kinetics, lasers (Mining drone or Xray) and fighter/bombers plus point defence. I recommend not using missiles on your space stations. Point defence can blunt their firepower too easily...either lasers or projectiles I'd say.