Having played this game many times, I thought I'd offer some advice.

To be honest, it's more fun finding stuff out for yourself, but if you want some advice, here it is.

Pirate Attack
If you have played the game, you'll know that there is a pirate attack pretty early in the game. You need to get some ships to defend Harmony before they arrive. It can be a hard battle, but if you follow the next few hints, it can be pretty easy, especially if you buy a Dragon beforehand.

Rescue Mission
Hire a S.I.N. agent, and send him down to the Soraya Nebula. I wont spoil the suprise, but it's well worth going there. Even though it's a long trip, if you do it early, you can get back in time to defend against the pirates, with the extra thing you find down there. I often buy a fox for this, to keep my bigger ships at home, but that's up to you.

Buried Treasure
Ok, I'm not going to tell you what's here either. But if you go to the lake/ocean in the middle of the planet, and do a survey just off the east coast (see image) you will dig up something pretty worthwhile. There will be a few messeges concerning this, but you do WANT it. Well you dont need it, but it's a help. No need to mine here though.

More Buried Treasure
From the bottom of the ocean, you can see a strang looking ridge, well follow that ridge almost to the end, and start a survery on the south side (see image). This time you'll find some odd crystals that you can dig up (Do it). The guy from D.I.C.E. will contact you and offer to buy it from you. Someone told me that if you keep it you can make some extra weapons, but I never noticed it, and you get a HEAP of money for it. So it's worth selling. You should be able to buy a Dragon before the Pirate battle if you do this a few other mines.

Just before you get attacked, Keif Bai-ley from the planet Pihzda will ask for help, because he is under attack. I always liked this guy, and would have loved to help him properly, but if you split your fleet you'll have a very hard time in either battle, and I dont think you have time for your ships to get back to Harmony for the next fight. But, if you send a really small fleet (maybe just one fox) and retreat as soon as you enter the battle, Keif Bai-ley is really appreciative, and gives you stuff. It's a bit cruel, but helpfull for you.

Research Boffins
I hire all the researchers I can. If you design a weapon, you can buy it REALLY cheap. So it's well worth it. Also, if you having nothing else to do, sit on the reasearch screen. Research projects go a LOT faster if you're watching them. I dont know why.

Extort Katrina Vannes from the planet Tool
First piece of advice - DONT! Nothing else to it, I did it once, and I was screwed. You can get some money for it, but you cant trade with Tool anymore. That wouldnt be so bad, you can build your own weapons and trade with D.I.C.E. still, but you cant buy any more ships, cause Tool is the only place that makes them. Very bad move.

I'll add some more when I think of them. It's been a while since I played the game myself.