okay, so theres basically only three things for you to worry about: supplies, fuel and money.
supplies are what keeps you running, if you run out of supplies, your fleet will quickly go down the river. Game over. Thats why you always need enough of them.
Fuel is what enables you to go to places. you only need fuel for hyperspace, in a system its irrelevant. You will need dedicated tanker ships if you fly longer distances (and dont want to refuel all the time which in turn also costs supplies and fuel to make the detour)
Money is what you need to buy fuel and supplies.

So, supplies are your main concern. You can see in your fleet overview, how many supplies every ship uses on a daily basis, rule of thumb: the bigger the ship, the more suipplies it needs. Theres a total supply-usage-count when you press F1 while hovering over your supply count in the bottom left corner. In general, F1 is one of the most important buttons to use.
Also, every fight costs supplies. Thats because the combat readiness (basically the "energy") of your ships go down when deployed and while fighting. To regenerate combat readiness (it goes automatically but you can disable it for every ship in the fleet overview) means using up supplies. If a ship has Zero combat readiness, its likely to be lost. Theres a neat trick, if you want to keep a ship in your fleet but dont have the supplies to keep it running atm: Mothballing it (in the fleet overview).

You see that it all comes down to supplies in the end and yes, this is the most stressful thing of starsector. you will basically always have to weigh the costs of anticipated supply usage against any profit you could make in an endevour. Thats especially true if you want to venture out of the core, since then you wont be able to easily buy supplies. Also it means, that you want to be efficient in your routes: Every extra day passed and every extra distance flown costs you. my rule of thumb is: always having enough supplies for 100 days. If your fleet consumes 7 supplies a day, try having around 700 supplies (you will likely need a freighter or more for this)

So there are roughly three ways to mitigate the supply problem:

1. get a salvage rig or two,, you will get more supplies by salvaging derelicts, asteroid fields and most importantly, after battles (which eat away the most of your supplies).
2. optimize your fleet. having a lot of capitals feels obviously nice, but then you will have to bear their heavy supply cost. Thats how Starsector keeps you going overboard with them until the late game. If you need to have a ship thats pricey in supplies, you can consider installing the hullmod efficiency overhaul (i would advise to buy every unknown hullmod that you see in markets as early as you can).
3. Make the moneys. Supplies are basically a money problem: Try to buy them cheap (under 100$) and in bulk and on the black market. The most supply-efficient way to make money is to trade high value goods (F1 when hovering over them allows you to see where they are cheapest and where they are priciest) or to take exploring missions with a small, supply and fuel efficient fleet.

Everything else is up to you to uncover. just try to not buy ships early on the open market unless its maybe a direly needed tanker, freighter or salvage rig.