Hello Norsehound!
I'm afraid you've gone head on into, what I think is the most difficult singleplayer mission. At least it's the one I've had most trouble with. (Finally beat it on hard approx 1 year ago)
For the singleplayer missions there is a way, not cheating exactly, but your manipulating the game somewhat. I'll pm you that one if you still really stuck
When the scenario starts I'm sure you've gotten the basics down, with getting more ore and setting up your base out of the lava's way. (My take on this is just to build straight east from the CC towards the mining locations over there)
I think you can go up until about 6-700 marks before the computer starts getting serious. In this time I suggest you take good care of your base, pay attention to morale, research upgrades for your buildings, stockpile some ore, and set up vec factories to cover the 6 entrance points. (I used 4 vec facs on 3 locations. 1 by my initial base, 1 to cover a 3 bar common down south and 1 right next to my rare mine(the closest one).
Please note that you don't have to keep the active at all times. Use them to reinforce your troops in a tight occasion, or to replenish your troops after an attack, otherwise keep them idled.
My suggestion for weapons is simply:
Early on: Micro's (Upgraded ofc)
Before Tigers: EMP/Micro Lynx groups. Though get ESG/Rare asap.
Late game: EMP/ESG Tigers. (If your quick enough to utilize them, place some ESG lynx right next to the entrance points, and let them fall back slowly to cause some damage before Eden groups reach your defense lines)
In late game, it might be a good idea to keep an extra spaceport with a EMP missile on aswell, in case your defense lines get breached.
A few other tips: Don't research unnecessary morale stuff, turn the game speed down, get as much ore as you can defend.
If you need some more exact locations of where to put defense etc, let me know.