Hello, I've recently purchased the game and was very excited about it, I loaded the game up and enjoyed the opening cut screen and such, after that I looked around in the options and saw they where lacking but was like, okay its still in beta so options are lacking, started my first game and played though to round 456 on a medium sized map with max AIs on gifted and won a conquest match, here are my toughs on the game play so far.
1) First off I do not like the new Save/Production/Research interface, Its very hard to make exactly what you want, Also I have a suggestion for it, To add a way to automatically keep your income at a point, like for say you want to always earn 5 credits a turn and it will balance it out automatically and you select the dominate spending like production or research.
2A) Colonization is quite.... bland, I would like to see more into it then just researching a tech to colonize a desert or ocean world and such, it would be great if you could add like atmospheres to the game that limit the colonizing faction on income, food and the likes until they take on a lengthy and costly project to convert the planets atmosphere to something they can breath.
2B) This also makes it where the different races can be more unique as not all races should or can breath oxygen, as well as the Yor not needing it all together (unless they do)
3) I dislike the fact that your shipyards have to keep building something or you can't end the turn, there should be a option to send it into idle mode.
4) Anomalies, I know its still in beta and more events from the anomalies will come but if they are anything like the last GalCiv 2 events they will be very bland, What I'd like to suggest is that they are to be spiced up, like adding a space monster or a swarm that your survey team unleashes onto the galaxy, one event could be a monster that is extremely powerful but very slow, massive hit points but no defense and ballistics as weapons, another could be you found a flight of swarm, this could range from 12(small) to 100(massive) bugs that will hunt out any ship in the area and will act as a swarm, never getting to farm from each other, also you could find the "queen" of the swarm witch launches a event that spawns massive amounts of the swarm all over the map.
5) Ground combat would be wonderful instead of the press the invade button and be done with it, I miss the old ground invasion from another game called Space Empires V, that game was great, it could play out just like with space combat where they fight and fire at each other as groups of soldiers, vehicles and air craft, or could just be a swarm of the mixture until all are dead from one side 
6) The Ideology system is a great touch to the game, I like the idea but think that it is a bit unbalanced at the time and needs a bit of work, witch I am sure that you are working on it at the time.
7) When designing a ship that is already pre-made it would be great if the modules already on it wouldn't disappear, some times it nice but other I just want to tweak it a little to my needs.
8) Targeted Terraform, This idea would be where when you terraform a planet and get a extra spot on it, you can select where you want it to be, from the available spaces that is so as to not enable a planet to be too powerful, just tiered of getting a spot out in the middle of no where.
Well thos are my thoughts on the game play of the game so far, I look forward to the updates and the full release of the game, I have been a bit fan of GalCiv from the start and am really thankful that you are adding muliplayer into the game as well as I am grateful for you taking the time to read my post.