First of all, good choice and don't just listen to what I or anyone else says, this game does generally allow for a large amount of playstyles and many strategies are entirely valid. That being said....
A few general comments:
Its good to learn the armour types and the damage types of the different unit archetypes. This enables you to build counters to what the enemy is using and to combine different ships into a force capable of dealing with a large range of strategies. These can be found here: https://forums.sinsofasolarempire.com/177682.
HuntingX has also made some excellent posts including efficient build orders. You should note that these work best in small games and aren't always the most effective in larger FFA and team games. These can be found here: https://forums.sinsofasolarempire.com/303701.
Multiple fleets are good as is attacking on multiple fronts. Destroy factories and repair bays first if you can and labs are key targets.
You should generally be trying to gain more planets all the time but not to the extent that it stifles your economy. Generally your starting capital a 4-6 kanraks is enough to claim planets if you send your capital in first to tank the damage. Personally, I concentrate on asteroids firsts, then terran/desert then ice/volcanic.
Infrastructure and Defence:
I have disagree with superfingers comments however, basically for the reasons he said. While civilian infrastructure is a must and you should get it immediately and trade ports can be useful if you already have the tech, building anything else when its not explicitly needed is, in most cases, a waste of money for the simple reason that you don't need it. Always have good recon, always scout and this should let you know when a planet is going to be attacked, allowing you to upgrade its defences.
Emergency facilities is useful if you know that planet is going to be attacked and you're not certain that you can deal with the fleet but having it on a planet which either won't be attacked or won't be until you're dying anyway is a waste of money.
You have the right idea with defences, minimal is generally better unless its a very large game, you have a lot of spare resources, its a key planet or if its a choke point. Against AI, a large amount of defences can be useful but against a player, they'll simply go around them, hit them from afar with LRM/bombers or wait until they can overwhelm them all at once.
Repair bays however, are a definitely worth it if the planet might see combat, particularly in the early/mid game. A few turrets can also be useful to buy you time since they're fairly cheap.
Hanger bays are good but they're also very expensive. Worth getting at choke points and key planets if you have the cash spare but only if you do.
Units:
Our scouts are excellent and used in conjunction with a number of the phase space researches Vasari can have excellent recon. Additionally, always grab neutral extractors with scouts when possible. They're the best unit for doing so.
Skirmishers shouldn't really be built first since they're expensive and easily countered by LRM. As such, most Vasari players will build a military lab first and research kanrak assailants. I find that skirmishers can be a good mid/late game unit when used it reasonable numbers. Particularly to counter flak, to hunt down carriers and for additional damage against capitals.
Kanraks are awesome and in most cases should be probably form the bulk of your fleet. The phase missile upgrade is great. On large games I will often upgrade the research line to its full. They counter light frigates, have excellent range and damage in addition to being able to punch through enemy shields. They're most vunerable to flak, carriers with fighters and heavy cruisers, all of which can be countered with skirmishers and the following two units.
Subverters are wtfpwn (their teleport and stun ability can be quite easily chained to render very large groups of units useless and vunerable).
Enforcers should be used to provide additional firepower if its needed, basically when the enemy has a lot of heavy cruisers as well.
Tech:
I don't like to state one BO as the best but generally, you should be build a military lab first. After that, civilian labs can be good or you can rush to a particular type of ships. I would generally say however, that on anything other than a large map, its generally best to only build 2 civilian labs before concentrating on the military line, this enables you to colonise ice and volcanic planets as well as providing you with some basic econ upgrades but since Vasari trade ports are tier 4, they're not nearly as good as the other races' in small games.
Cases where 3-4 civilian labs can be built without having to worry include when more advanced ships that your kanraks can't effectively deal with aren't being used and when you have the time to establish an economy before the fighting will begin.
Capitals:
See: https://forums.sinsofasolarempire.com/309106 and HuntingX's posts. Also, the Space Whale is mighty.
