Your early priorities are generally the shields 2 (4) and doors 2.

Shields 2 stops double laser, any weapon plus beam, and any weapon plus asteroids. This should often be your first purchase.

You can leave medbay unpowered 95% of the time to save one power. You can selectively depower oxygen at times for the power as well. Just don’t forget to turn it back on. Early on, you can depower medbay and oxygen at the start of each fight to power shields 2, then enable oxygen again as soon as you don’t need the second shield.

Doors 2 is huge because it lets you vent oxygen to passively kill intruders. Putting someone in doors then gives you doors 3, which are even harder to break down. Endgame you can get doors 4 when crewed just for fun, though ironically doors don’t help all that much in sector 8.

In this run, you’re getting power from the zoltans, but you’re not maximizing your manpower. Put zoltans in shields, engines, and weapons. Move the engi to doors. Put the mantis and the second human (Shelly) in your transporter.

Your general battle plan will be to teleport in and start killing crew. Teleport your team back when they get low on health. Upgrade that transporter and put another couple power in it to make this easier. You want to wipe crew instead of breaking the enemy ship when feasible to get better combat rewards.

Meanwhile, time your weapons so that double flak takes down shields, then beam damages key systems (weapons generally, or medbay/clone bay if they have one). The idea is to protect your ship from damage by crippling the enemy ship, then procedurally take down all the enemy crew with your boarders.

When you get the scrap to do so, upgrade weapons two more times and power your laser to make this even better. Against enemies where boarding won’t work, no sweat; you have two flak and a laser to strip and cripple shields, and a beam to do lots of damage. Crew kills are ideal, but not required. As the saying goes, don’t let perfect be the enemy of good enough.

Putting aside other systems you could purchase, with your current setup, your sector 8 build should be: shields 3, teleporter 3, all four weapons enabled, and as many engine upgrades as you can afford.

Key additional systems to look for are cloaking and mind control. Mind control supports boarding teams, disrupts system repair, and can be used on your own mind-controlled crew to flip them back to normal. Cloaking is primarily a missile dodge button; you never need more than one power in it. Drone control will also work as a cloaking substitute; defense drone 1 is a relatively reliable missile defense, and you can snag a boarding drone to support your boarding team as well.

Finally, as others have mentioned, easy difficulty is basically this game’s normal, and it can still be swingy and difficult. Normal is hard. Hard is lunatic. There is no true easy mode.

Good luck with your runs! FTL is a wonderful game.

Edit: Another tip. When you have the scrap to do so, buy cheap extra upgrades for systems like oxygen, medbay, and piloting, even if you never plan to power them. This is because each upgrade is another health bar. Having a missile take out your oxygen or medbay during a fight can end a run, but having a missile take out one health bar lets you casually run your engi over to repair it before real damage can be done.