For the most part, you will not need to buy or upgrade anything considering how weak your enemies are in sectors 1 and 2. I personally reccomend Saving your scrap and not upgrading anything until sector 3. If you do happen to come across a store. You will have 3 Priorities.
1: Upgrade Defenses
2: Upgrade Weapons
3:Upgrade Utilites

So save your scrap throughout Sectors 1 and 2, do not upgrade anything and only buy drone control and cloak if you come across it.
If you come to a store and you have 2 options, Drone Control or Cloak, If you have a defense drone, get Drone control, if you dont then Get cloak. I cannot express how many Defense Drones and Cloak have saved me so I reccomend you try to get them the second you can.

At this part, if you do not have an Ion Bomb, Drone Control, or Crew Teleporter, I highly reccomend trying to get them at this point as they will be very helpful. I would also try to get to atleast your second shield this sector.
For Sector 2 I would reccomend on Upgrading your defences Including:
Piloting (For Dodging Attacks)
Door Systems (Get Blast Doors, this is the part where Intruders will start to invade you.)
Your Shields (Try to get you second shield atleast.)
And once you have upgraded everything else, Upgrade Your Engines.
If you have any left over scrap, try to get atleast level 2 sensors because they only cost 25 scrap.
I would also reccomend you start to upgrade your reactor a little bit because more power allows you to use more things at once.

When you first enter Sector 5, I reccomend you try to get to atleast your third shield.
After That, try to upgrade your offenses, Look for more weapons and drones. and Try to upgrade your weapon control. Also this is the sector that I reccomend you start to upgrade your medbay, try to get to atleast level 2, if not 3. Intruders are going to start teleporting onto your ship, if this happens, vacume out every part of your ship except for your powered medbay, it will force them into the medbay where they will fight your crew while your crew is already healing. I also reccomend you Sensors to level 3 in this sector.
Finally, upgrade your reactor some more, try to get to atleast 3 rows of power in your reactor.

Alright, if you have gotten to sector 7 and you DONT have 4 shields by now, GET THE 4th SHIELD NOW!!!!! IT IS VERY IMPORTANT FOR THE FINAL BOSS.If you do not have a crew teleporter by this Sector, I highly reccomend you get one, its very important for invading enemy cruisers. By this point I reccomend you try to hire as many crew as possible while upgrading your teleporter and your Drone Control (Hopefully you have Drone Control by now) Also, its not really needed, but you should try to upgrade your oxygen. Finally Try to upgrade as much to your reactor as much as possible and use your leftover scrap to upgrade or buy whatever you can as the final boss aproaches. One last thing, you must, and when I say this, you MUST have your piloting and Engines fully upgraded, they are very imporant. When you get to the final boss, go all out, by now you should have a good enough crew to send your crew onto theirs while attacking them. from the outside. The Ion bomb is very useful for the final boss and really most bosses before it because it can really screw over the enemy shields. Once the shields are disables, Burst lasers are very good for dishing out damnage.