So, just finished my first game in a while.  I played on a gigantic map with lots of planets, few resources, few anomalies, and 4 Genius opponents.  I played a custom version of the Altarian Resistance.  Here are the things I noticed.

1. At Genius level, the AI was much better than I at claiming planets and resources.  Once everything was claimed, I ended up with the smallest initial empire.  It's good to see this, it means that the AI is working.
2. I was frustrated at not having the resources to build cities.  Farms seemed useless, I always had a food surplus.  Shortly into the beginning of the game, I got a morale boosting tech, and then I set my tax rate to 100%, where it stayed the rest of the game.  I only had science and production planets.  I find that having half of the game economy mechanics not working a bit of a disappointment.
3. Despite not building influence buildings on my planets, I gained 29 planets through rebellions.  
4. Two different nations gave me all their planets.  One of them was actually at war with me at the time, one was not.  This whole mechanic of 'Oh, dear me, I'm Poland and Nazi Germany is attacking me!  I'm going to surrender to Panama' seems a little odd and unrealistic.
5. I'm always a bit amazed that it's much easier to make a big ship fast than a small one.  For the end game, I designed two fleet types.  The first was had 21 moves and consisted of tiny, small, medium, and 1 huge flagship (lots of auras).  The second had 49 moves and consisted of one huge flagship and the rest being mostly large but occasionally medium ships.  I planned for the slow fleets to defend my territory while the fast would ignore enemy fleets and clear their planets for invasion.
6. It was late in the end game when I declared war on my sole remaining enemy - the Iconian resistance who owned 75% of the galaxy.  My ships were kinetic/shields.  They had nothing but tiny ships, but they had two varieties:  missile/shields, and energy/armor.  So some of their ships were glass cannons that did tons of damage and died quickly, while the others lived forever but didn't do much damage.  Had they made missile/armor, I would have been unable to defeat them at all.  Still, their fleets were all limited to 7 movement, so I could engage them on my terms.  But I'd made a mistake in not researching multiple defense and weapon types, (and in taking long enough to do it that my enemy had modified their fleets) and I appreciated the game punishing me for this.
7. At the start of the war I had ~8 slow fleets and ~12 fast ones.  The first two turns of the war saw me destroy 30% of the enemy fleet, but I lost 30% of mine.  My slow fleets did better at the harder fights, but I lost some of them every battle, especially the tiny interceptors.  I discovered that the role system was important and I'd clearly messed things up.  It's not very easy to understand in game, especially prior to combat.  My fast fleets had less trouble with this, as they were all capital ships.
8. With my slow fleets having to constantly wait for reinforcements, my fast fleets had to hit whatever they could.  After two turns, some of them were looking ragged.  The flagships always were attacked last, so I had an abundance of these still.  On turn 3 I found myself combining two fast fleets into a fleet with two huge flagships and a single large ship.  This fleet went on to defeat 4 of the largest enemy fleets that turn without a scratch!  I was clearly on to something, but what?
9. Further investigation on subsequent turns led me to discover that the auras from my flag ships were stacking!  A single flagship had a dodge rate of 80%, but get a fleet with two flag ships and that went up to 115%!Somehow I was still occasionally taking damage, but with my self healing-hulls and massive hit pools, there was nothing they could do.  And so I began creating double flagship fleets and building more flagships, etc.  It looks like all auras stack, I was seeing it with shields, movement, range, fleet repair, etc.  With this in mind, I think my best ship design would have been a fleet of 55 tiny ships with Inertial Field Projector, Statis Field Module, Acceleration field, Field Disruption, Barrier Field Generator, and 1 pulse cannon.  They would have been dirt cheap too (236 construction).
10. With my fleets being as fast as they were, it took me 8 total turns to destroy the entire Iconian military and a few more to complete the ground invasions.  At the end of the game, an interesting thing happened.  I started getting 700 tourism income per turn, per planet.  I had 361 colonies, and 306,674 tourism income.  I hit the cap, which is 1,000,000 credits.  I'm guessing that tourism simply hasn't been balanced for large maps with lots of planets.  Just another reminder that I was playing a game without a working economy.
11. Tested out the 55 tiny aura fleet.  I ended up with a fleet capable of 1622 total damage with 117,975 shields.  Individual ships have 29.5 kinetic damage at 10325 range, 2145 shields, 1405% dodge and 359 moves(turns out smaller ships ARE faster afterall!).  Still needs more testing to see if the the incredible range means you don't need the Field Disruption or the Barrier Field Generator... if so you could put 5 more pulse cannons on with that mass, increasing the damage up to 177 each.  Probably I'd end up going with making 10 ships that have these modules and 1 cannon while the other 45 just have 6 cannons.