Hey there,
first to my background: Played quite a while ago: MOO2, GalCiv2, Armada 2526 Gold, Endless Space, and most recently Civ 5 (played 582h mainly MP) of which I will take a couple of examples.
I played this first steam alpha build for 110 minutes as steam says and here is my feedback so far. I know this is still an alpha and some balancing things will be fixed later on anyways, but I think it won't hurt to mention them now already. I also don't care much about "but it was like this in GalCiv2". Even if it was, it doesn't mean it can't be improved.
Game Creation:
-There are no tooltips about the technologies the races start with
-The Opponent team number you select feels weird. When adding all opponents, they all have Team 0. But as a Player I do not know if that means "no team" or if they are all together in team 0. Imho this should be like in civ with an auto increment on adding an opponent.
Sound:
Effects aren't in yet, so no comment on that. Not sure if it's the same music as in the last game, in any case: love it. ^^
Graphics and Performance:
The Graphics are fine though I would love to have even more detailed "maps" of the planets, but I will elaborate on that later.
The Performance was rather bad. While it was playable upon scrolling you could feel the game stuttering, starting right at turn 0 (Phenom X3 ~2,8 GHz, 6 Gig RAM, GF GTX 260)
Starting Conditions on Planet:
The starting conditions are extremely random which is something I already didn't like in GalCiv2 but which gets even more important now when Multiplayer is supported. You can start with some huge bonuses on your starting planet, and you can even start without a single tile enhancement (happened 1 out of 3 times). Also the adjacency bonus will probably have a huge impact - if your starting spots are separate, bad luck. So imho you should think about ways to make the starting conditions on the homeplanet equal. After that you can kinda adapt. E.g. for resources there could be a "budget pool" of 3. And each +1 value costs 1. So you could have +2 Production and +1 Food or something similar, but everyone would have at least the same total at start even if it's not 100% equal. This is btw also a huge factor in Civ 5 which does not work at all (Someone with starting next to 3 salt resources has a huge advantage over someone starting in the tundra having beavers...)
After the Homeplanet you will be able to adapt into the direction you need. But if your home planet is inferior to everyone elses you are crawling behind right from the beginning.
Planet View:
-The graphics of the planet do not represent what type the tile is. I had 3 spots in the artic: 1 Greenland, 1 Prairie with +2 farming, 1 Mountain. My capital was in the ocian. I am not sure at which Date GalCiv 3 will play. But I doubt humans will build citys on or under water yet.
-I mentioned before that I'd like to have more detailed graphics. First the other planets look very blurry compared to earth. But even the earth could get some more details, so that you have a better feeling of being on an alien planet, breathing toxic air. 
It's not bad as it is now, but the best feeling of an alien planet I had in Master of Orion 2, where the big background picture made you feel you where "on" the alien planet.
-There aren't any tooltips in the planetary statistics. I need to know exactly how these 6 Production were calculated, so that I know if the population has a bigger impact or I should rather focus on building factories for example. This is something Civ 5 does extremely well.
-The Prairie Land has no bonus and seems weird when even mountains give bonus to wealth (which seems weird as well)
-Adjacency Bonuses are a great idea and it will be quite fun to think about the layout. But if you implement them you should implement them well. E.g. something like "buying tiles" in Civ 5 might be great if it can be implemented in some way.
But the most important thing is to get a better overview: "Where should I build this factory?" Make a couple of buttons to display bonuses. E.g. a "Farming Bonus display" and when you press it, you will see a "0" on all tiles, a "1" on all grassland, a "3" on grassland with +2 farming, and a "2" on a +1 grassland with a farm next to it giving it +1. This would help a lot.
-The buy/destroy/cancel buttons seem not untuitive as some of them relate to things on the upper list, some on the one below, some on the map. Also when "buying" things you can see the price you need to pay - but you don't see the money you have.
Movement:
-The graphical display of movement could be improved like with a radius showing the tiles you can reach within that turn (like in Civ 5).
-in the strategic view you can't tell which unit is selected
-One question I asked via SpaceSector.com was about the simultaneous turns and their execution. Seems like I misunderstood what you meant with sequential: Everything you plan will be done right away like in Galciv2 or Civ5. It is not a "everyone plans" simultaneously and then everything gets executed at once-situation, like in a football manager game for example, where you set up your team, click on ready and then everyone has their game at once.
This has basically no impact in Singleplayer. But it will be a pain in the ass in multiplayer:
The way it is now (and the way it is in civ 5) it will be very dependent on how quick your pc loads and how fast you are at clicking when doing movements. I will give you some examples from Civ 5 which will apply in some form in GalCiv3 MP as well:
Player A and B want to get to ruins. The player who clicks faster gets them.
A unit discovers a city with his first movement point but gets in range, if the other player attacks him with his city fast enough, he will hit/kill the unit before the other player can use the second movement point.
If a unit was badly hurt in one turn, you must be very fast in clicking to flee with it in the beginning of the next turn, if the other player is faster then it will get lost.
This system makes the whole combat extremely absurd and somewhat broken. Civ5 tried to compensate that at first with forcing to play without animations. Later they implemented the option to automatically swith to "real turnbased" if there is war.
When I played with/against friends we solved that by houserules when at war: We all plan simultaneously, but someone has to move first each turn and after he said he is finished, he is not allowed to react within that turn anymore.
But it would be much, much better if the game had an alternative system alltogether. Which is hardly possible in a system with One Unit per Tile system with very landscape dependent battlefields but it's very well possible with Space 4X games.
The Next Turn transition
-There should be a different button for "move planned ships" when it's not done yet instead of a normal "next turn". Next turn should be displayed when this would really end the turn.
-there should be an event log showing what happened when the turn starts
More Information about Planets/Suns
One of the coolest things in space games for space enthusiasts is to have real world references. It would be great to not just have "habitable 5" but detailed information about the type of the planet, the atmosphere and maybe some information about what this planet is good for. An earth like planet might be good to grow food. A planet like Mars might be good for mining (more tiles with mining bonuses) or something similar.
Same goes for the Suns. When you can see the suns anyways on the map, then display the color. Make them clickable and show something like "Stars from this type are very young and it's unlikely to find planets around them" or "Stars from this type offer the biggst habitable zone, you might even fight life in this system". I think endless space did a good job with that if I remember correctly.
Opponents:
-I shouldn't be able to see what my enemy crafts (guess this is for beta testing)
-my enemy tried to "zerg" the Fighter ship I found with scouts - which had no weapons.
Invasions:
There were just numbers and a result. Would love to see something more detailed here. Invasions in MOO2 were pretty cool, where you saw little people fighting each other on the planet surface. Not that you could influence anything, but it looked cool.
Anomalies:
Some anomaly bonuses should be "locked" away until some turn. Like faith huts are in Civ 5. Finding a "Lost Gunboat" with 6 attack and 5 defense is cruel if enemies don't even have the very first weapons.
Early Game Defense:
Right now you don't have any weapon technologies when you start the game. You can't buy any fighter at all.
Now if player A researches fighters, builds /buys one and sends him to B, B is screwed. He won't be able to do anything in space at all until he researches weapons as well and builds a ship. Until then everything in space will die. This could be solved by having a very low range starting ship with some cannons you otherwise can't build, so that you will need to keep it around your homeplanet for defense. Being helpless for 10-20 turns would just be bad. No issue in Singleplayer of course if you can just tell the AI to not do that. But devastating in multiplayer.
Edit: Typos
Little Addition:
It's currently possible to see the event triggered by Anomalies by the Anomaly name. This keeps away the surprise and it might be of advantage to save a couple of turns to not even move to the anomalie as you might know from ealier (or a wiki) that it's not of a big benefit.