Ah, Derelict. I won my first multiplayer 1v1 on this map. Good times, good times.
This map heavily favours the Vasari faction, in my opinion.
"Long-Range Jumps" enable you to jump directly from one star to any other star (explored or not). The wormhole on this map can be safely ignored because the "exit point" is next to a star anyways. There's no point to expending a lot of money to use a back door which is actually right next to the front door.
First of all, this map has a lot of randomness in it. Most of the wealth is in neutral gravity wells, so you'll need to send colony frigates (scouts if you're Vasari) to capture and hold these. Scout early and find out where the resources lie, and start claiming them. The second piece of randomness is the colonizable planet in your starting solar system. It is not always a volcanic. It could be an ice, volcanic, desert, or terran. You need to find out what it is and how heavily guarded it is in your opening move. A highly-guarded volcanic is a worst-case scenario, a lightly-guarded terran the best.
The trouble is that heavy militia might make it too much effort to take early on. Similarly and ice or volcanic would require civic labs, which on a map like this is very tough to support, but puts you very close to long-range jumps. The alternative to taking your initial planet is to make a bee-line for the middle star system and grab an asteroid there. It's a long ways from your homeworld to the middle star system, so you'll want to set up a frigate factory there to produce units.
As Vasari, you can have long-range jumps with two labs, but regardless of what faction you play you'll probably want to tech it pretty soon. This will enable you a lot of mobility over the map, and enable you to both attack and defend distant locations very easily. This will enable you to harass the enemy's homeworld and keep the pressure off of you in the central solar system. If you need more opportunities for expansion, the third solar system might be worth your time, but if you can lock down the central solar system in your favour then the AI is pretty much screwed at this point.