Psudo, your 2nd idea is bad for medium, and horrible for hard.
1. First off, keep restarting the game until your units end up where you want them. They are semi-randomly placed at the top of the map
2. Build near where you start. On the black ground, there is a 3 bar common. Start with this. DO NOT build your whole base on the black land though. The volcanic eruption will obliterate anything you put on the black.
3. There should be a single common mine nearby, and a double common on a spot where the grey/black/orange land meets. Expand to these as soon as the lava whipes out your mines. Careful not to loose any trucks! These'll provide a fair bit of ore.
4. To the East of you, there is a rare ore mine. Its not too far, just tube to it. (This is why you don't build in rocky area. No nearby rare)
5. Get Microwave and stickyfoam tanks fast, they can delay attacking armies quickly and effectively (especially the stickyfoam) Work on getting EMP and ESG out. Once you have these, mass them. They'll effectively defeat most Tiger attacks Eden will put against you.
6. If you can rushkill the Eden base in the South West, this will really make things easier. Build there. Its the 3rd last area to be infected by the blight, which will buy you precious time. Plenty of ore there too. If you do take out this spot, you can abandon your old base. You won't need it, and it won't be long for the blight to whipe it all out. Just idle the structures (not a bad idea to just deconstruct them. If you leave most of them, tho, the AI will beeline for that old base first, until everything in it that is not a morale building is dead. Use this to your advantage!)
7. If you can, however knock out the FIRST Eden base, and decide to ignore the second, its attacks are easily managed. One vec fac can only build so fast. This is also the last spot to get infected by the blight!
8. Don't forget the Microwave rush! Unupgraded, the microwaves will obliterate an Eden lasers. Why? Eden's laser does 5 points LESS damage then a Microwave. Granted, half of that is due to concussion, but Light armor blocks very little of that anyway (if any). Reserch Heat dissipitation and Turret powerplant with scout drive train refit, and you have a killer. About 40 of these things will mow through the Eden 1st base. You need to get them very early though, before mark ... ah... about 500? I find its easier to build a group of about 10, then move them in in 10s. The AI will simply stream tanks at you, so they're easily managed. You only need to build up enough to take on the guardposts.
9. Don't forget colony management! Otherwise, you'll lose anyway.
10. REMEMBER: The objectives are to LEAVE NEW TERRA. You do NOT have to whipe out Eden! Theres plenty of time to get all the starship bits out before you have to deal with the blight. On medium, Blight comes about mark 2500 I think.