The hardest part is getting started since you have to get ramped up pretty fast. You cant hardly fight fully equipped ships let alone multiple with figher escort with 900 credits to start with. As such my priorites are thus:
1. Efficient weapons. Energy cannon plus a particle cannon with autofire if u have 6 tech. both 800 range. Add particle cannons as you can afford.
1b. 2 Fighter Bays. These guys are awesome for clearing the first few sectors of fighters and decent for quite some time afterwards. They provide "clog" to stop rockets and all sorts of projectiles.
2. Get a Defend Station quest by rejecting others. While many avoid them, I like to start with 1. The idea is that I know where another station is now, and when I get there I have cleared a few sectors, maybe dragged an enemy big ship with me, have another one there already and then the Defend one spawns. Assuming the station isn't total crap (WHY are there unarmed stations around anyways?), you can take out several ships pretty easily, letting the station repair you while you body-tank the station.
This tends to get you really FAST cash/tech and maybe a drop if lucky.
3. Try to be flexible. Dont have a set strategy in mind. Adapt based on what you pick up. Using human weapons for long is a loser.
Dealing with Wanderers - They usually have missiles/rockets. Having the Fighter Bays clogs up the works and you generally want to jump right on them at beat them up at medium to short range. You want to stock up on point defense bolters with autofire and 1 hull boost...usually ALL on one side for 1st map (unless valiant ship,etc with front firing guns), and face the enemy with that side always.
You usually do NOT want to outmissile them on the 1st map...HOLD ONTO their best rocket/missiles and once you can MASS them, go for it on the next map.
Celestials - On the first map, just outgun them and start stealing/buying good Ion Cannon Mark 2 to beat them. Fighter bays provide valuable clog to block their lasers/deathrays/megaplasma if they get any.
On 2nd or 3rd map, you need LOTS of fighters of some kind....either bolter fighters or lots of bombers to get in the way and eat their damage.
Dump your Point defense and go with almost ALL shield boosters, with tech invested into them. This stops their guns pretty well at medium range.
OR, you might have tons of missiles by then which is a good strategy...tho you still struggle vs closer foes with their deathrays.
Trolgars - Stay away from them if they have flak cannons! They usually have awesome projectile cannons which you can liberally steal from them and pair with a shield-shredder and kick butt.
They dont usualy have ANY shield-penetration so they are trivial at medium/long range since their shots bounce off your shields. EZPZ.
Shiellah (sic) - They tend to have random stuff.
Unknown - Similar to Celestials except WEAKER. Go figure. Use the CLOG strategy with maxed out shields.