As everyone else has said, get speed, then turning, then cargo, then fuel. You can throw in a few mixes, like getting a second cargo thing before your last turning jet, or a few turning jets in the middle of speed upgrades, those were more a guideline than a hard rule. Then crew, and not before. You’ll eventually need more to refill your ships or lander during long trips.
For your specific question: Don’t use your flagship for anything but running, if you can avoid it.
If it’s a Kor-ah (Black) ship, run for your F’in life up until you have a much better ship. You can take them with the Spathi Eluder (which is much bigger than anything else of it’s manuverability), but it takes time.
If it’s a Kzer-Za (Green) ship, either of your sub-ships will have no problem, and the Zot-Fot-Piks are surprisingly useful here.
The Earthlings can (just barely, if you use gravity wells right- don’t accelerate afterwards, it’ll just slow you back down to your “max” speed) outrun them and have a point-defense weapon that automatically takes out any little ships they send, and the “fire-it and forget” homing nukes have a range great enough that you don’t even have to be facing them, you will eventually win, probably without a single loss, but it takes time. Also, they tend not to send drones against things with point-defense. Actually, the cruiser’s boring and almost useless, but there are strategies to work around its many, many problems.
The Spathi BUTT missiles do essentially the same thing as the nukes, but you can fire more than two on a full battery. Your regular gun and spinning without thrusting should deal with the drones. This, however, just takes skill and puts you at risk.
The ZFP’s just kick ass once you’re used to them. Their guns have a tiny bit of range on the Spathi, and they spread. The Kzer-za’ll actually fire drones at you up until he has about 5 men left, and you just turn around, sit in one spot, and shoot, and you’ll pick them all off. You are faster and more manuverable, and once he’s wearied, either escape and put in the Earthling, or fly around his back and go in shooting and hope you kill him before he turns.
You can tell I’ve played through this game enough times that I did a “never buy ships after the first month” run, can’t you?
Here’s one fun thing to learn, that makes sense but you never think of until you’re forced into it in super-melee- Earthling Cruisers annihilate the Orz. The Point Defense lasers kill marines in one shot, their actual shells in two. They move just enough faster that turning doesn’t matter, and the nukes, when you actually survive long enough to use them, are almost the ultimate weapon. You almost can’t be hurt by that otherwise awesome ship with your otherwise almost useless ship that really should be sold.