Seven planet system? I presume you're talking about point blank.
The unfair AI is actually surprisingly easy to beat here. The key is to be viciously aggressive. Send a couple of frigates to capture the asteroid next to your homeworld, but your capital ship should be heading straight for the enemy. The ice planets are traps; ignore them and attack. You have to win fast on this map or the unfair AI's resource cheat will start to kick in and you'll be in serious trouble.
The easiest way to win this scenario I find is distraction. Try to get the enemy to follow your capital ship while your frigates make a beeline for the frigate factory. If you can knock out the frigate factory, you pretty much win right there. Doesn't matter if he has twice the income you do, he can't spend it and you'll kill his current units. Just keep your capital ship moving and the enemy will have a hard time catching it (Sova works best here).
In terms of units, it's all about the LRM. Unless the enemy actually reaches carriers, you have little reason to build anything else. A repair bay at home is a good idea in case your capital ship gets damaged. You can then retreat and repair and be back in the action within the minute.
