Usually you have to stablaize morale first or your population drops way too much. It takes too long to recover from this if you let it happen. Nursery and University are also priorities. I've tried playing the level a few different ways. I find stabilizing morale first with residences and agridomes before worrying about research, nursery, or university tends to have slight better results than going for the research first. But only slightly better most of the time.
Always go for the 3 bar mine first.
If you want an easier time defending, or killing the enemy bases, it really helps to get an early strike in on the base in the top left corner of the map. You can also try a strike on their main base in the middle, although this is somewhat harder to do succesfully. I found attacking from the south before the lava cuts you off tends to work. Usually I leave the main base in the middle for last though.
You can of course ignore killing the other bases and just defending, but you tend to have to defend against a lot more if you ignore their bases. If you can't get an early strike in, you may just want to do this however. Once they start getting too dug in, you can't really break through with lynxes, at least not laser lynxes. At that point is usually best to defend until you get tigers and thor's hammer. Just don't forget the importance of well placed EMPs, and Acid Clouds can also be quite helpful sometimes.
I find getting rare ore from magma wells takes too long, and the rare ore in the middle is too far and too exposed. I usually prefer games where the mine at the bottom is rare. (If you can't see it at startup, it's rare). If that's the case, then you may also have to worry a bit more about common ore. The mine to the right isn't too far or too exposed but it does take a while to tube to it. It helps to start tubing early and to get a second earthworker to help in this. Also, it sometimes help to establish your presence here first and then worry about expanding to the 1 bar in your base later in the game. It's easier to defend the mine on the right if you're already there and don't have to worry about incomming attacks when expanding to it. Even if the mine is a 1 bar mine, it'll be very helpful to have. You should get at least two smelters on any mine, preferrably three, but you might have to wait for workers or resources. Use two cargo trucks for each smelter, and learn to position the smelters close, but not so it causes crowding. (Usually have the bulldozed regions touching, but not overlapping the mine).
You may also notice that the sooner you get weapons, the sooner you'll be attacked. They also won't be particularly agressive if you haven't researched weapons. They might just run through your base and attack things on their way through, but usually won't stop to attack. If you want to play a defensive game, this can be helpful to know. Spend the early time on colony research and ignore weapons research. Just don't ignore it too much. Maybe play one game to find out just how long is too much. :unsure:
Don't forget about Metallogeny early on. If you're stuck on a 1 bar mine, this really helps. You can build up a fair bit of reserve ore before the yield drops down to minimum. Keep in mind that the yield will drop however, and don't let the reserves lull you into a false sense of security. If you're stuck with only 1 bar mines, and your population isn't hurting too much, researching the GORF stuff can lead to more research that ups the yield a bit more. Just keep in mind that once you research it, you need to keep a GORF operational to keep your morale up.
Learn to spot attacks and try to kill their units one at a time as they come trickling in. The AI is really dumb about this. You can be outnumbered, with weaker units, but still win if you get theirs one at a time. Learn where their staging points are for their armies and learn where to position your units to take advantage of this. Note that is you occupy a staging point, they tend to group up at an earlier one. So you might want to defend just a little bit back from one of their staging points, and move in to beat them there once you see them coming.
Also, for resource limited games, don't forget that a repair vehicle can be used to repair vehicles up to half health. This can make what few lynxes you can afford to build last a fair bit longer. Just make sure this doesn't occupy too much of your time or it'll become counterproductive. By keeping the number of lynxes up, even if they're all hurt, you keep your firepower up. Having 3 nearly dead lynxes is usually much better than having 1 lynx with full health. Especially since repairs are fairly cheap.
Lastly, if you really are stuck without rare ore, you'll need to eventually take the middle open area. You can't launch a spaceship without rare ore. Having three common mines should allow you to build enough EMP and Railgun lynxes to manage this. You may find yourself in a much more defensive position much of the time though, but it is still doable. Try and get tubing towards the middle as early as you can before the attacks become a problem. When you finally do take the middle, you'll want to be getting rare ore as soon as possible. Having weapons that take rare ore will greatly enhance your ability to defend the middle. It also doesn't hurt to have a few rare ore storage silos back in a safe place in case you lose your semlter. That way you can at least keep some of the mined rare ore to build better weapons to retake it with. Taking the middle is also much easier if you've removed the base in the top left early on since you'll have less directions to defend from.