This is my first post on these forums. I've viewed a few helpful threads, but now that I've beaten the game, I want to share what I did and what I upgraded in the hopes that someone else might view this and get some use out of it.

Apologies for the dark image as I took this hastily after (surprisingly) winning
Let's start off by saying that in my experience the Engi Type A is the best. I tried the Type B, but to be honest I found myself struggling in the beginning with the Type B. I think I can chalk this up to turning on Autofire. You're using the Ion weapons, so you have nothing to lose turning on autofire. In my experience, aim for the shields. The shields are always my top priority. You can even spare yourself the drone parts in an asteroid field by just spamming the Ion weapons.
Here's a rundown of my upgrades. Starting with Shields.
Three Shields -- In other playthroughs, I'd waste precious time and scrap on four shields. Three is plenty on Easy.
Five Engine Points -- This was sort of where I'd put points if i didn't need them. If I did, I'd just take them out of engines, and put them elsewhere. It does benefit to just keep the points in there as it boosts your general evade %.
One O2 Point -- Never really found oxygen to be a problem. Especially since your crew heals throughout the ship
One Teleporter Point -- The teleporter was not used too much in my playthrough till the final battle. The weapons destroyed me in prior playthroughs and I found that teleporting in a Rock Man and a Mantis (or two Mantis') really did short work of the weapons. During the second fight I focused on the Drone Room. All in all, you'll want to use the Teleporter to make short work of whatever your biggest threat will be that round.
Three Cloak Points -- Especially during the final battle, being bombarded by missiles or lasers is not uncommon. Luckily you can see the signs that these are about to happen. Now, you'll still want to use the teleporter but also remember to use cloak to evade any weapon fire headed your way. The bonus points in the engines certainly help with this as well.
Five Weapon Points (Three for Ion Blast II and two for Burst Laser I) -- Now I'm sure this will extremely vary with each playthrough but I found that aside from the Ion Blast, all I needed was a Burst Laser just to do some more specific damage as (unless someone knows better) I don't think you can tell drones to target specific (sub)systems. The drones will be your primary offensive tools, but it doesn't hurt to also have the Burst Laser.
Six Drone Points (Four for Anti Ship II and two for Anti Ship I) -- I understand a lot of people go for the defensive drones, I found that with the shields and cloak, I didn't really find it a neccesity. Since I had those two defensive options, it gave me room for these two. Obviously the Mk.II is your best friend here, but the Mk.I also does some considerable damage. Even in some of the last two sectors it was a cake walk with these two.
I did max out all subsystems, but that's also because due to my Augmentations, I wasn't blowing a ton of scrap on drone parts.
Augmentations:
Drone Recovery Arm -- A very important augmentation that keeps your drone supply self sustaining. Great for saving scrap.
Engi Med-Bot Dispersal -- Default with Engi Type A. It's great for keeping your crew alive in longer skirmishes.
Shield Charge Booster -- Another essential in my opinion, it keeps your shields up which is great for the whole game, but during the end boss it becomes a real life saver.
Other quick tidbits of knowledge...
...buy the level 2 doors subsystem first (before anything else) as it helps if you get boarded...
...Try to get Zoltan crew members as they free up more of your power supply...
...Make sure you also have a few Mantis' on your crew as they make for great boarding parties...
...Always sell missiles for scrap...
...If having a huge ship wide fire or a large boarding party, I'll pull all the crew into tight quarters and vaccum out all the air from the ship. Wait until the O2 returns to repair your systems...
...It may be a dick move, but never accept surrender unless there's a weapon or augment. If you accept a surrender you'll almost always receive less scrap, so might as well bear the fight for a few more seconds for extra scrap...
...Remember to pause! This game will destroy you if you don't pause. At a certain point you don't need to, but even I'm not there yet. Pause, evaluate, and then attack accordingly, then resume and watch the destruction...
Best of luck! Again, I just felt like doing a post-mortem and evaluating my strategy for others. If even one person walks away readied to beat the game then I'll consider this post totally worth it. Thanks everyone and feel free to ask me questions if you'd like to know more.
As for me...time to tackle NORMAL.