I have plenty of crystal coming in, but my metal is slow. I have all metal and crystal production fully upgraded, but I guess I don't have as many metal extractors as I have crystal. I keep having to buy metal which is annoying.
If you see you aren't going to be getting much metal income, and you have at least a small amount of space, often it's a good idea close to the beginning of the game as TEC to research the first two metal income upgrade rates. That's sometimes a good idea even in competitive games, because that initial metal income research is tier 1 and is so cheap.
As TEC you can also research something to significantly decrease buying prices from the black market. In longer games where you have a significant resource imbalance it can help a lot.
All of my planets except 2 have a starbase. The 2 without are in the far back with one route connecting them to one of the planets that has a starbase, so I didn't worry about them (though I did build two hangars, two turrets, and a repair platform for them). A starbase for 11 of the 13 planets is probably overkill, but after all the trouble I had with rebels and enemy fleets last game, I wanted to fortify everybody. However please look at the map and tell me what you would suggest when you talk about choke points. That will help me in future campaigns.
I'm going to guess that Galatia in the south is your homeworld, because you said you have a lot of crystal income (allegiance effects). I'm also assuming that your enemy was red up on Caldiera, whom you conquered and took over.
If I were you, I would have started the game by scouting, and then sending a colony cap to Caladon or Krypton to kill siege, colonize, and build turret(s) while your scouts were looking around to see where the enemy is. Once I found that the enemy was up in the north, I'd beeline for the choke point on Persia, or I might even completely bypass it and go for Mirrin if my scouts saw that the enemy cap/fleet was going in a different direction.
Given that I knew how spacious the map was beforehand, I wouldn't go for trade and would research the starbase ASAP. After killing the siege on Mirrin and colonizing I'd immediately build a frigate factory, get a constructor, and build a starbase there. (I wouldn't even go for trade ports)
Once the planet was colonized and the frigate factory was under construction I might send the colony cap out to Ennomos or Cygania if my scouts showed that the enemy was in either of those gravity wells. I would bomb the planet if they tried to colonize, or would attack the colony frigate if the planet hasn't been colonized yet. Even the moderately advantaged AIs (hard and unfair) probably won't have a large fleet by this time so my capital ship would probably survive long enough to kill the colony frigate or to bomb the planet out.
I'd also research repair platforms and repair upgrades and build them on Mirrin just in case my capital ship offensive fails, which would be quite possible.
I might build a capital ship factory on Mirrin and build another capital, which would continuously attack whichever planet the enemy fleet isn't at (the asteroid, the desert, or the homeworld) and then retreat to repair once the enemy fleet came in. With continued cap harassment like that with my two capital ships, the enemy might even be too distracted to ever come attack my starbase. This would work for a few minutes until my starbase was strong enough to manage their fleet.
I would then build trade ports everywhere, and then would research Pervasive Economy, while the enemy would probably be attacking my starbase and leveling my caps. I'd probably send the colony cap back in the other direction to colonize planets I'd skipped. From that point you can basically do anything because you have an almost unlimited amount of funds, given your trade ports and Pervasive.
The enemy would eventually colonize Cygania again - when they do that I would hope to have a similar choke-point starbase up on Ra-Shalom in case the enemy decides to split part of their fleet and go that way.
One thing that has been a royal pain are homing mines. I initially moved a scout close enough for the reveal mine ability, and I watched my strike craft automatically shoot them down which was great. However, when I moved my scouts close enough to several other homing mines, my strike craft just sat there. I tried to select them and order them to attack the mines, but nothing. Eventually they did, but it was really weird. In the end, it took so long to eliminate the mine field, that I took the heavily armored Kol in, activated the Adaptive Forcefield (for shields) and Finest Hour (for quicker repairs) as mines hit it's hull. I also had my Dunovs nearby to hit it with shield boosts as it got smacked around. Then I had my Hoshikos go crazy with repairs to the Kol's hull. This allowed me to quickly clear those fields, but I don't like doing that. Is there another way?
Homing mines are annoying because often they place themselves where it's impossible to clear them, like in the middle of a star or inside of a planet or something. I generally clear the ones I'm able to clear and ignore the rest.