I'm a Vasario player too, and you will find that they have great firepower and mobility, but are more challenging then the TEC.
Early Game
Don't expand too fast and don't do too much research. It makes you vulnerable to attack and can kill your economy. Upgrade planet infrastructure as soon as you capture a planet.
When you start the game, make 2 or 3 scouts, buy 100 crystal and build a capital ship factory. Make a coloniser capital (jarrusul evacuator, better known as the "Space Egg")
While your scouts are exploring, you have to capture any neutral extractors lying around. This gives you an early game economic boost.
Capture the nearby asteroid, but make sure to kill the neutrals guarding the planet first.
Don't do too much research early game. Get assailants. Spam these early game. You can rush and defend with them. Making more frigates is more cost effective early game, but I usually get hull and phase missile upgrades early game.
Do not turtle. Expand and be aggressive, but don't overdo it. You should ignore tradeports and get refineries about 20 mins. into the game.
Mid Game
Don't look for a fight mid-game. Focus on economy. Expand cautiously. Research carriers, subverters and enforcers. Mid-game you will have a relatively small fleet because Vasari ships are expensive, but tough.
Do not get equal numbers of every ship type. The idea is to get a flexible fleet that counters your opponent's fleet. Get assailants (early-midgame)and carriers, subverters and enforcers(mid-late game) Mix in a few others like sentinels and overseers (mid-late game).
Late Game
Late game, you fleet should be heavy on carriers and enforcers. Subverters are important as well and give them the Distorsion Field upgrade. Overseers also help to keep your own ships alive. Don't upgrade the Overseer's other abilities. You should not have as many support cruisers as other ships.
Phase stabilizer nodes are strategically important. Get them. Build one at each of your border planets. They allow you to phase jump to any other planet in the star system that also has a phase stabiliser. This make it easier to respond to an attack on your empire.
Tips
Fighting carriers and spamming carriers is very important in the latest patch.
When fighting carriers, make carriers yourself. While you are building up a carrier force, make sentinels and skirmishers.
Make 1 sentinel per enemy squadron.
This means you will have 2 to 3 times as many sentinels as you enemy has carriers, but you fleet will still be cheaper.
You should not normally make skirmishers, but make 2 skirmishers per enemy carrier and give them the Interference ability if you are struggling against the enemy carrier spammer.
The Kortul's Jam Weapons is good at level 3 and the Skirantra Carrier's Repair Cloud and Micro-Phasing Aura help you own strikecraft stay alive. Do not bother with bombers. Make only fighters much of the time.
Do not make seige frigates. They are worthless. To take over planets, just get the Space Egg (coloniser capital) and other capitals.
Do not leave abilities on auto-cast. Usually, capital ship abilities should be microed. Microing abilities unlocks their true potential.
For example, you have a capital ship that is getting focus fired. Use the Skirantra's repair cloud to heal that unit and get your Overseers to use Reactive Nanite Armor on that unit to help keep it alive.
Another example. You are being attacked by a huge enemy fleet. Your fleet is nearly as big. Use the Kortul's Volatile Nanites ability on an enemy ship. Once your Vulkoras Desolator is in range of that enemy unit, activate Phase missile swarm. Watch enemy ships go bang.
I hope I haven't given you too much info, but I do hope it was helpfu;
Cheers,
