Honestly couldn't tell you if there's a method to finding where you get certain upgrades

I just cherry pick the upgrades I can get, make some cash, move to another system and do it again.
If you're into combat, I suggest the power coupling get upgraded asap - it's what governs how quickly you get power to your systems/weapons/engines, along with what you put your settings at (arrow keys if you're on PC default). Getting weapon upgrades helps too - the beam laser is nice, and if you're looking at kinetic (which is a good idea, most of the fight will be chewing through hulls) it's easier to start out with a better fire rate (8/sec?). I tried a cannon, with .5/sec - disaster lol. Might work for you -shrug- also, you can check the fitting of the weapon - fixed means a lot of aiming accurately. Gimballed means it's got a fitting that gives it a lot of movement, typically with computer tracking so you don't have to aim so much or be facing your target exactly (think 45-90 degree arc). Totally awesome.
Though with kinetic weapons you have to buy and rebuy and rebuy ammo

which also means cutting some hunting expeditions a bit short (3-6 1v1 fights?).
Regardless, welcome and good luck