Hi I purchased starfarer last night, and I had a hard time breaking away from it once I started, it's got the Mount & Blade in Space feel for me. Speaking of M&B the coolest thing in that game was working for a kingdom then stabbing them in the back and joining another. I hope in the final version such diplomacy will be possible? And a few more major factions besides the Tri-Tachyon and Hegemony. Anyways as everyone else is talking about other great features they would like to see I believe I will focus on ships.
Now I understand from the current design of ships, that a Build-it-yourself custom ship design interface is out of the question. That would be really sweet though.
First off let me state that I absolutely love the current designs of the ships! Especially the Capital ships they are truly awesome. As this is an Alpha I'm sure the final version will feature many more ships and ship variants.
I think every catergory could use at least 5 more unique ship designs, then add variants as you please. Since this is a sci-fi game and the millions of ship designs that the human race has dreamed up, this should be no problem.
Fighters- This Catergory should have the most diversity in ship designs. Players should be able to chose between 4-5 different types for Fighters, Bombers, Interceptors, and Multi-role. As of this moment Interceptors and Multi-role are severly lacking. Then you can add whatever amount of Specialty Fighter-class ships you like, as you have already done with the Wasp Drones, and the Advanced etc.. Also a Gunboat design would be cool ala starwars cygnus gunboats and missleboats which are very very slow but carry a huge payload.
In Destroyers We could use a few Heavy Destroyers. In Cruisers we need Escort Carriers, as well as more Carriers and Heavy Cruisers and possibly an Interdictor Cruiser (Prevents the enemy from retreating also inspired by star wars). As far as the Capital Ships go obviously more and varied Battlecruisers, more Elite/Super/Heavy Carriers and a Mothership(Can have no shields, very little firepower but the biggest hangar in the game, and maybe it could be saucer shaped?
), Several More Battleships and maybe a Super Battleship(Yamato). I'd also like to suggest a New Class The Dreadnaught. You can make these either More Powerful Yet Slower then a Battleship, or just better in everyway depending on design choice. In our history Dreadnaughts came before Battleships and were Behemoths, carrying oversized armaments, and chugging along at a snails pace. Also the word Dreadnaught just sounds infinitely badass.
Anyways whatever you decide I'm sure this game is going to turn out great, especially with such an awesome and supportive community behind it.
Also a last minute addition, and this may be a little hairbrained but maybe a Transport Ship design which carries marines and if you purchase them and defend them in battle, it can guarantee you a boardable ship after every battle. These ships would be very very weak, and unarmed.
and when you couldn't refit ships for the missions 
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