I've just gotten this game as of 0.9 and having an absolute blast so far. So: Here's my feedback (in order of importance):
1. It takes too long to understand the concept of avoiding larger fleets in the beginning of the game. A big part of this is that the UI doesn't give you much feedback as to another fleet's relative strength. Later on, when you learn the various hulls and can understand a fleet just by looking at the ships, it all becomes clear. But in the beginning it can be frustrating. I would suggest having some indicator for new players when mousing over another fleet that indicates whether you can reasonably engage it or whether you should run away.
1a. Also I would decrease the fuel cost of emergency burn for small fleets and increase it for big fleets.
2. The player ship's "speed" indicator in combat makes no sense, it only shows the overall speed without showing the direction. It would be very useful to replace this with (or add) a 4-directional speed indicator showing speed forward, backward, left, and right. That way it's apparent at a glance whether you're advancing or retreating relative to your other ships.
3. I've changed "combatSpeedMult" in settings from 1.0 to 0.5 and this made the combat work way better for me. It should be an in-game setting I think, for people who can't keep up with normal speed.
4. After I bought my first cargo freighter I noticed that my daily supply usage also went way up. But storing more supplies takes up cargo space, which require more freighters, etc. etc. This becomes a real irritant for long-haul trips, where I always feel like I'm either about to run out of supplies or going to lose critical salvage. It seems like it would be better if supplies had a separate inventory cap and 0 weight, the same as how fuel and crew works. Maybe there could be some dedicated supply ships also, so that all 3 fleet resources work the same way and there's more thought to be put into how to balance your combat and non-combat ships within the 30-ship limit.
5. It would be nice to have some way to put resources into hunting down those pirate/path bases that keep raiding my colonies, instead of having to hunt for them personally.
5a. BTW there is currently a bug where "Show system infos" from the sector map will display pirate/path bases even if they are not discovered yet.
6. "Shift" key aligns the front of the ship to the cursor, but some ships need to fire broadside (Conquest, Odyssesy, etc.) There should be an option in the "Weapon Groups" dialog for each ship to align to left, front, or right.
7. There should be a way to spend resources to entrench nav buoys/comm relays/sensor arrays points so that some 1-ship enemy fleet can't reclaim them. The problem is that the fastest ships in an enemy fleet will always escape and cannot be eliminated by the player fleet (Tooltip when trying to pursue: "The enemy fleet is too fast for your forces to catch up to"), and then that fleet will make a beeline to reclaim these structures and claim them for the enemy. For now there is no defense against this and so no reason to claim these points.