Start with the cap ship factory and then go with the extractors.  every second that the cap can be out in a map this small is worth while. take the asteroid that is adjacent to you, you can take it with just the akkan, but make sure to kill that siege frigate first.

also, it is easier to have his fleet come to you for the big battle as long as you have 3-4 overlapping repair bays on your planet, so keep the fight, or at least your ships' side of the fight inside those purple circles

This is an incredibly easy win for you.  I suck when compared with most people who play online, but I can win this easily with the AI set to unfair.

The first thing you should build is your capship factory.  Queue up your first capship as soon as you start building it.

My first advice is not to build the akkan on this map.  Akkan is good for colonizing.  Thing is, this is not a big enough map to justify the colonizing cap.  You can just send a colony frig up to the connecting asteroid and take that, and that will be all you need. 

BUILD THE SOVA.  Get missle platforms on it as your first choice.  After that, alternate between heavy strikecraft and missle platforms. 

ALTERNATE CONFIG: Get embargo.  Send sova to enemy homeworld, start embargoing.

Other than that, just start spamming the frigate of your choice and hit his home planet in a rush.  You might want to drop 2 mil labs and tech to lrm, and just lrm spam him to death.  Otherwise, just go cobalt spam.

If you play vasari, the win is quite easy.  Drop 2 mil labs, tech starbase, then drop a starbase on his homeworld.

So I ended up winning using everyone's advice...

Akkan vs. Sova - I built an Akkan since I already had that built before I saw the Sova advice.  I did end up building a Sova in late game though.  I can see how having a Sova first would make sense.  A Sova could have cleared away the neutrals around my nearby asteroid just as easy (easier really) and I'd then have a colony frigate come in to claim it.  That would leave me a stronger offensive capital ship at the start.

Claiming Terroritory - There were two ice planets begging to be colonized on this map and I did research the appropiate tech to do so.  However, I never ended up making it that far.  With an early pirate raid (my fault, I had enough money to bribe them onto my opponent but didn't) followed by my opponents first attack, I had to become more military minded right away.  Even if I did get around to claiming them the benefits of owning more planets really wouldn't have helped much.  My resource flow was already sufficient and there isn't enough time for lots of research or fleet building on a small map like this.

Repair Bays - Fighting within range of my repair structures is just beautiful.  Really makes early game battles at my planet so much easier.

Being a Wuss - So they attacked me and I destroyed their fleet and nearly destroyed their capital ship until it jumped away.  So I took my fleet and followed.  I finished off the capital ship and destroyed the remenants of their fleet around their planet.  I ended up pretty beat up and was still contending with their defense structures when another enemy frigate was built.  I figured it was time to retreat, get repairs and come back to finish the job.

I didn't really understand how long a capital ship can survive and felt a panic when the game told me my capital ships shields were down.  In hindsight I had plenty of time to stay and finish off the defensive structures.  But I didn't stay and next time I went back a large portion of the fleet had been rebuilt and there was a new capital ship awaiting me.  By this point I had researched some better frigates and started the battle anew with a rally point set on the enemy planet.  I also had built a Sova and won the battle decisively after awhile.

By leaving early I left all their extractors intact and their planet undamaged.  So their fleet was nearly destroyed completely, but they had their strong resource flow intact so rebuilding was a cakewalk for them.  A rather obvious, but when you are in the trenches of battle it can be hard to see straight

Replay the game.  And, as Kyle Reese said to Sarah Connor in The Terminator, "Do what I say!  Do exactly what I say!  Don't make a move unless I say!  Don't make a sound unless I say!  Do you understand?  DO YOU UNDERSTAND?!?!"

1) TURN OFF PIRATES, because they won't help you get better at playing the game (they really won't) - in fact they will hinder your development as a player.  Unless you just plan to play single player free for all type games, turn them off.

2) Here is your build order as TEC (start right away, should take 10 seconds to queue everything up): colonizer frig, capship factory -> sova, extractors, 2 military labs.

3) Send colony frig ALONE to the roid next to your planet.  Go right in, capture the roid, then attack the siege frigate with your colony frig.  Meanwhile, build a defensive turret directly in front of the siege frigate, as close to the roid as you can.  Then upgrade the riod's population, and queue up all extractors.  If you did this right, the turret will kill the siege frig and the cobalt.

4) As soon as it rolls off the assembly line, send the sova straight in to enemy homeworld, and start bombing his planet.  Have the missle platforms set to autocast.  If he has a carrier there, set sova to build fighters.  If he is building lrm (or illums or assailants), set to fighters.  Otherwise you might consider bombers.

5) Research lrm.

6) Set factory rally point to enemy planet.

7) Keep mashing "build lrm" button.  Fleet up as necessary to keep building lrms.

These instructions are all that is necessary to win in short order.  Note that there is no dilly-dallying or wasting of time with any of this.  The game starts and you build your factory and extractors and labs, queue up the colony frig and capship factory, and queue up the research right away.  As soon as the frig pops out, send it to the roid.  As soon as the capship pops out, send it to the enemy homeworld, building strikecraft and selecting missle platforms as it is moving.  Lrm should be queued up as soon as any funds are ready, and a continuous stream should be pouring towards the enemy hoemworld in short order.

You should win the game quickly.

You do need to cover for the starbase construction time if you do that, so I recommend skirantra with some skirmishers (skirmishers are tougher than assailants, but deal considerably less damage). Vulkoras is great for bombarding the planet, but it lacks in direct combat and support.

The solo colony-frigate colonization exploit that Agent of Kharma mentions is perfectly viable and a great minimalist approach, though sending three or four light frigates will also work.

That's more true in 1.17 than it is in the current version.  A Marza that finds itself up against a carrier capital ship will get minced.  If you pick Marza and your enemy picks a Sova, Halcyon, or Skirantra, you're in deep trouble.  I don't pick Marza first anymore as a result.

It might work against the AI, since it picks its first capital ship randomly, but I find it's safer with the Sova.

Also 1.17 specific; the Marza has definitely fallen out of favour and the Akkan is now the king of the TEC fast colonization blitz.  While still a tough tank and great at clearing planets, the economic edge of the colony cap is too much to ignore now.  Good Akkan players can colonize way faster than the best Marza players.

Marza has fallen from grace in 1.18 and onward.  These days, early strike craft are the norm, and the Marza has no fighters of its own, leaving it way too vulnerable to carrier-capital ships, and the vastly improved Akkan offers way better quick-colonization capacity.  With this, the Marza's only shining point left is raze planet and high damage output.  Powerful as that is, it's not enough to redeem it and it's now regarded as a second capital ship pick, not first.