Well, generally, it's all about the ship you fly to be perfectly honest. I remember spending quite a bit of cash on upgrades when I first played, as i jumped into a Rhino (Freighter) and found the story missions impossible.

The best ship (early on) is a dagger, but trying to afford it is very tough. The patriot is a reasonable substitute though.

After that, its a case of needing the best shield possible (check the types out, I went with the highest capacity type ones - forget what they are) and the best gun types for your shooting ability. I always went with lower rate of fire but higher damage, due to the fact that one hit = the same as about 2-4 hits with higher fire rate ones... where typically i'd miss a few hits.
Then it's use of nano bats and shield bots. The shields tend to regen after about ten seconds, so once they are down i usually fly in unpredictable circles, moving the mouse everywhere, to avoid fire. That way they tend to come back online by themselves with little damage taken. IF i'm getting hammered, then i'd use a regen - otherwise, just dodge a lot, and hope.
Use nano bats whenever i get to half hull or so.

The most important thing i found, though, is the engine kill + thruster. Without a thruster you tend to die exceedingly quickly. Use it to attack, dodge, move, everything. Use it in bursts as well.
To keep the bursts working, i tend to use engine kill - you "glide" through space, in the direction you were moving, but can spin about and turn the ship whilst still going in the same orignial direction.

This way, when enemies are incoming, i engine kill and thrust. Speed is therefore about 200, and you're sliding through space. Start shooting, use strafe and thrust to avoid fire at this point (wiggling mouse does nothing) to hit incoming.
Once they go past, turn the ship around whilst still in engine kill (you may have to repeatedly engine kill) and then thrust towards them - opening fire.

In the event that they are pounding you, as long as engine killed (so sliding), keep hitting thrust and altering your direction as you do so, moves you around quickly, and keeps you from flying in a straight line.

It's hard to describe, for engine kill get used to the sound of not having an engine running, otherwise you may find yourself turning the engine back on and coming to a near standstill instead of sliding about. It'll take a little practice, and can be dangerous in minefields due to lack of real control, but it's the best way to survive.

By Bretonia you should have level 3 shields or maybe even level 4 (from the Lane Hacker base, I think). You should have bought or tractored in some good guns too. Also, are you using countermeasures? Drop plenty of them to avoid the missiles. Mines can help too. Dump them so the folks after you will run into them. (I don't bother with missiles. Mount another gun instead of a missile launcher.) Get a Crusader as soon as you can. It has considerable fire power for that part of the game.

When you are in a dogfight, make sure you stick on the same target until it is destroyed. If you go chasing after everybody, you'll get nowhere and simply be blown up.

I find it best to fight at a fairly low speed and use my thruster to hang onto a bad guy's tail. In Bretonia you are up against some ships with powerful guns, so try not to go head on too much. Some factions (e.g. Mollies) tend to have guns with shorter range, so try to use that to your advantage.

Whenever I've played the story line (unmodded) I always worked my way up to a better level of ship and loadouts. Considering some weapons were not yet buyable because of a certain level, I'd go wreck hunting for weapons and mount them on the currelt level ship. (the weapons that could mount on it).
As for encountering those nasty npc's, when I got myself into a pretty lethal situation and had to escape, I'd kill the engine and thrust away from them.. then turn my ship to face them as I flew backward. (the npc's wouldn't know what to do and slowly loose distance from me until I was safe enough to turn around and go into cruise)

If you want to get through the story line in a breeze (for the fun of it)..
activate the "nearly Indestructable Shield Mod" and "Beam Weapon Mod" .
With that, you could go through most of the game in a starflyer (except where radiation zones will eat you alive)

Xenos, i neglected to mention that Xenos used to drop some nice weapons for when you first start. Colorado (i think) Silverton field, inside there you'll meet Xenos. try to toast them - you can pick up their bat/bots they drop, and also some nice weapons. Mount their weapons, good damage ratio for their class.

Thanks everyone. I've been using the engine kill trick and I've also come to realize that there's better equipment and ships hidden around the game than I'd previously realized. I'm doing much better, as a result. I appreciate all the help.

Sorry if this is redundant, but try and get a Defender from the Battleship Missouri in the New York system. Personally I pefer that over the patriot. Also, I belive it comes with a level 4 shield. You can buy it right after mission01, but I'd reccommend doing one regular mission first.

Oh...Yeah...a cruise disruptor (from battleship YUKON next to Los Angeles) is a nice addition to the Defender when you have to defend Willard Research Station from the incoming Reinland Bombers. That'll slow them down for you.

I concur with the others. A freighter just isn't useful during the storyline except for certain specialized purposes (eg. long trading runs where most of the NPCs are neutral or green to you). I always go with the fighters (HFs or VHFs). I find mixing a 4.00/5.33 weapon with several 8.33s to be a good compromise, as I tend to not do as well as others in precision shooting. If you can possibly get them, get the Gas Miners' Guild weapons. They're the best 8.33s you can get for the money, IMO.

Yeah, those class 8 & 9 GMG skyblast A & B are shot per shot some of the most powerful colonial weapons. Until you get to latch onto some class 10 nomad guns like the blaster (rx4) and cannon (rx3). (high damage and excellent range with no power usage)

Don't forget Rogue weapons. Call me crazy, but they are much more formidible than any weapons early in the game (with a little energy conservation) and are relatively easy to get ahold of.

Deck out Mule with a full arsenal of Drails and Raphaels and you are a force to be reckoned with. I personally appreciate rapid weps.