I usually don't pay that much attention but here is what I read and I do.
1. Ships repair automatically. They repair much faster with stacking repair techs (basic repair, advanced repair, etc.) and micro repair bots trade good.
2. Ships repair on the move but maybe faster if they are kept stationary?
3. Ships repair faster in orbit than out of orbit.
Sorry I haven't watched with a notepad handy but most of the time, ships (to me) are either field-ready or they are not. If they are not ready for action, then try to stay away from combat and slip them into orbit if possible.
When you look at the military race, ships in orbit allegedly get more military rating points than ships out of orbit. And, attack factor boosts military rating more than defense factor. I am pretty sure this is legit for 1.05 but I don't know if anything changed for 1.092 or will change in 1.1 due next week. Hope this helps. Good luck.
i've always had trouble with repairing, i would basically just send all my ships out on suicide raids, destroying until they blew up. i would get a few level 2 ships, thats about it. then i started sending them into orbit around the closest system, and in a couple turns, even the most damaged ship was repaired fully, so putting them into orbit does help a lot.
Ships repair quickest in orbit. They repair when not in orbit - they do repair when they are moved and used, though it is much slower than when in orbit.
If you're a warmonger like me, repair is critical. Ships are expensive to replace. I typically destroy 150-200 ships on medium map while losing only 30-40.
I don't bother using starting picks on repair, but I do research repair technologies quickly. (I'm not sure it's worth it - I view Corvettes and lower as cannon fodder anyway.) Ship's repair themselves quickly in orbit so as long as you take a system quickly and park you ships there for a few months, you'll be fine.
Frigates, Battlehammers, and Dreadnaughts seem to have the best survivability for the price. In my experience, battle cruisers and battle ships are too fragile when taking on equal competition.
Military resources are a huge factor in reusing ships. A high attack reduces the damage ships take (so I research those techs as well). Finally, ship experience does have a noticeable effect...
Ships gain experience when they survive battles. The tougher the opponent they defeat, the more experience they gain. When you select a ship, you'll see a little experience meter at the bottom of the ship's description.