It's interesting that you do not use quickstart, much ebtter for novices. Anyway iw oudl say while building Cap ship Factory, also buidl the Crystal Extractor. Then after both are done build the 2 Metal extractors. Crystal is mroe improtant early. Also get the population upgrade for home ASAP!

Your order is off a bit.

You want to go for a culture center first.  The Advent get the best culture bonus in the game, and the increase from income pays for itself faster with culture than trade ports.  It is also cheaper to implement sooner (econ lvl 2, only one needed for 3+ planets)

Once you have 4 planet bodies, then you can go for the trade route, but not before - it isn't cost effective.

Your ship build has a hole in it - no strike craft support.  Your fleet would lose to a fighter heavy fleet.  You need some defense vessels or strike craft of your own.  You can get those earlier than the other factions (lvl 2!) and make more strike craft than the other factions.  Get some!

I also noticed you don't take advantage of one of the best parts of the Advent ---- SYNERGY! 

You will want to get 2 more capital ships once you have ~40 illums, the carrier cap and then one of the support caps.  The abilities work together on your ships great.  The amplify energy aura of the carrier will own everything, especially with an illuminator heavy fleet.

You're not alone; you've successfully identified the most powerful ability in the game.  It was nerfed (reduced in power) in a recent patch, so that nefarious status may no longer be valid, but it remains a powerful ability.

Good pick.

Now, I understand where you're coming from, but I honestly don't recommend this.  Sins uses a "rocks paper scissors" counter system, meaning if you build too many of one unit type you leave yourself vulnerable to its counter.  I strongly advise to diversify your fleet early and don't lean too heavily on the light frigate. 

For more detailed advice on colonization, I refer to my guide: https://forums.sinsofasolarempire.com/363623

Whether you want to go for military or economic tech first depends on your start location.  Especially with normal start (you have more leeway to pursue economic strategies with quickstart) there needs to be a wide distance between you and the nearest enemy for you to safely pursue civic technology early.  As a general rule, if the enemy is fewer than 7 jumps away, it's suicide to build trade ports early on.  The AI will let you get away with this because it isn't very good, but a player will show up at your door with a massive fleet and knock down your trade ports before they pay for themselves.

Trade ports are, in my opinion, overrated.  They have a huge capital investment requirement to become effective, as you need a long trade route (at least 4 or 5 jumps) to make them effective.  Even once you have a decent length trade route, it can take 15 minutes for a trade port to pay for itself, and that's before counting the effect of upkeep.  Late-game, trade ports offer you a strong way to bolster your economy, but early game they're way too expensive to set up and a good military player will show up with a strong fleet before your economy booms.

As has been mentioned, culture is a stronger investment.  This is because one culture center will affect multiple planets (five or six, usually) which is very cost-efficient.  Otherwise, your best economic investment is always capturing new planets and building extractors there.  This also gives you strong assets later in the game.

As far as defenses go, hangers typically shouldn't be built in large numbers.  They're great at chasing off small groups of enemies, but a dedicated assault force won't even flinch.  If the enemy comes in numbers, your fleet needs to be there to defend your planet.  No static defense in the game will stand up to a strong fleet (AI idiocy notwithstanding; it's legendary for its ability to get a massive fleet slaughtered by a modest but well built defensive line).  The best defense is a bank of repair bays.  These provide your fleet a place to retreat for repairs, and if they come under attack they can repair each other to buy time.  This allows repair bays to stall much better than any other type of static defense.  Since a good fleet will come with healing ability of its own, turrets and hangers don't really do that much.

For units, balance is the key.  An illuminator/guardian based fleet with a progenitor mothership leading it makes a great base, but you need other units to round it out.  Heavy cruisers, flak frigates, and carriers are great picks, even disciples with their ability to steal antimatter make great support units.  As far as capital ships go, try to get a variety.  A Halcyon is a great pick for swatting enemy strike craft, while a Radiance is great for disabling enemy capital ships.  Rapture (one of my personal favourites) and Revelation also have their place.  Advent works very well when you have all their special abilities on the field working in tandem.

I could understand if you need to clear several ice/volcanic planets in a row.  Those flak frigates get annoying to clear out.  However, if you take out all the other frigate types you really only need about 4 disciples, hardly 50 command points worth of them.  They won't help you take out a heavily defended terran or desert (at least not without unacceptably high casualties) and as an army won't do much to stop a LRF rusher.

Instead, I use a combination of LF and scouts for my colonization needs.  Eight scouts and four light frigates are usually sufficient for these purposes (that's 32 command; along with my capital ship that leaves 18 unused command, perfect for a neutral-nabbing missionary and some scouts that are scouting).  I warp in the progen first to aggro the militia, then warp in some scouts.  I focus my attention against the siege frigates first, then colonize the planet and redirect my attention to the LRF.  Once the LRF are down, I get my scouts out of there and bring in the light frigates to clean up the flaks while my progen cleans up any light frigates. 

For heavily defended deserts or terrans, you basically need to unlock repair bays if you don't want to go into upkeep or shell out a bunch of money replacing disciples, so you will have to get two military labs anyways in this case.