Thanks everyone! It's good to speak with others who have been there and can provide wise counsel. Frankly, the fleets you folks warn me about have me concerned.
I just intercepted my first Hegemony AI patrol when playing last night, and it was certainly the hardest fight I've had yet. Must have been six to seven capitals total, in two huge fleets with what seemed like an additional 40 or so ships - fought both simulataneously. I had six capitals and a bunch of cruisers and it was simply an exercise in trying to pull my ships out when they got down to 1/2 hull. Just before that I fought four, full-strength pirate fleets simultaneously and the two Hegemony AI patrols were at least twice as difficult as the four pirate fleets. I can't imagine what fighting the endgame fleets will resemble.
I had two Paragons, two Onslaught XIV, one Odyssey and a Conquest, plus several heavy cruisers, a couple Champion, a Doom, and a variety of lighter 22 point and 15 point cruisers. I think I was down to the last couple cruisers while two Capitals were still fighting when the Hegemony fight ended. Keep in mind all ships were flown by the AI and I have 10 at least 5 point officers, plus all my Capitals have two built-ins. I was limited to 240 DP at the time, which I have since raised from max 400 to max 500 to see if there's any improvement in the effectiveness of my fleets.
I'm kind of wondering where the improvement in capability on my side will come from. Certainly after the Hegemony fight I started building another Paragon since the tracking stats consistently show that's my highest damage ship, and I don't have any of the AI ships in my fleets yet, but I am maxed out on character fleet skills and on officers. Guess I'll have to do more exploration, find and capture some AI ships, find more BP's, see if I can get any Tachyon weapons, manipulate the fleet deployment size, and then go from there?