Some ships are trap options and should almost be avoided even on Easy, after meeting Oberon, unless you want to add a extra layer of difficulty or are a achievement hoarder. This guide assumes that you aren't.

(Ship ranking and tier list by Olga)
Good ships:
. Kaos. Suicide bombing is really powerful. I also modified my tactic after losing first battle to Tetsuo: I started selling the Brutal deployer as soon as possible; it let me use other squadrons except the Boomer drones, especially Frigates, because they were too fragile with 1/4 health. With more tactical variants I finished the Kaos playthrough easily.
. Excelsior. Just a universal ship which is comfortable to play. The only difficult boss was Tetsuo (I was lucky to find/buy 2 enormous ramming frigates and defeat Tetsuo and his 2nd sector general with them).
. Jericho. Not my favourite ship (requires kinda specific tactics with weakening enemies with non-direct damage cannons), but it wasn't very difficult to beat the game with this ship.

Debatable:
.Abyss.This ship has lowered prices in shops, but the most important thing is that Abyss has Boomer drones like Kaos, but the other squadrons (especially 2 Frigates) can be repaired and spawn with full HP. The good variant is to find/buy another 1-2 Boomer drones, keep all these drones Patched and pick an officer who makes Patched squadrons do more damage to unpatched ones. Another variant is to pick officers with Hull-repairing and/or Regeneration skills. Generally, this ship resembles Kaos, but with repairable units and more glass-cannon-like: AFAIR it has the lowest HP. This caused some problems in Chapter 3 (♥♥♥♥♥♥♥ stealth fighters and Abyss' slow respawning speed) and Chapter 5 (maybe, just bad luck).

Do not pick :
. Hammer. Slow squadrons and problems with reaching the enemy hull. The playthrough with it wasn't as difficult as the Geno one, but I didn't like it. The good thing is that it has many HP even without upgrading.
. Geno. Very fragile (even more fragile that Abyss despite having more HP). In Chapter 3 I had huge problems with dealing with stealth fighters' attacks. If you aren't lucky enough to get 3-4 Frigates and powerful weapons, you'll have problems (at least in Chapter 3).

What you want from a ship is at least one unlockable level of Fuel Mining at minimum. You don't really need more than one level of navigation radar. Offensive (squadron) power is king, and key to ending the fight, especially if you don't have to worry about Defense with an Officer that can repair your Hull, and another one that boosts squadron DPS.

If you're not that lucky, a Officer that boosts weapon reload is the next best option.

(Global Achievements showed for a long time that only Excelsior ever finished a run on Hard difficulty, I don't know how it is now.)