During this mission there are only a few light skirmishes before you can buy the class 5 graviton shield. To get through these easily:
(1) If you get a warning about an incoming missile, drop a flare. This does not work every time but often enough. If the missile is coming from in front of you the flare has little chance of distracting it; Shoot the missile or take evasive action (fly a hard curve away from the missile, drop flare, afterburn). In most cases you can out-turn missiles and they cannot catch you at afterburner speed.
(2) If an enemy drops a mine, try to shoot the mine down or dodge it. The mines are not very powerful but it is still a bad idea to 'collect' all of them with your shield.
(3) Do not take the enemies head-on; your shield cannot stomach what they can dish out with their main guns. Dodge a bit and then take them from the side or from the rear.
(4) Watch your rear. If you use chase-cam view then you can see when you get shot at from behind or from the side, and where the shots are coming from. Take evasive action as appropriate. If an enemy is chasing you then you can drop a mine to force them to manoeuvre, which can give you a few seconds of breathing space to finish off your current target. To drop a mine while under fire from behind, wiggle your tail a bit, turn off afterburner, drop mine, then afterburn. This is necessary because you don't want an enemy to shoot one of your mines while it is still within blast radius of your ship. Seeker mines are inexpensive and do a good job.
(5) When you are on the six of a Valkyrie, watch your shield strength. The Valkyries have rear turrets that can sting quite a bit but you can try strafing to throw off their aim.
(6) Try to stay away from cruisers and battleships until you are a better pilot. The fighters sometimes lure you near one of the capital ships when you are chasing them and the cap ships can really hurt you if you get too close for too long.