to you KSSSWM, great post.
As a Sins veteran, I've learned a lot since vanilla and Rebellion is a lot more diverse in terms of mid-late game strategies, but the basic early game is usually the same as it has been since the original release.
Here's my 2 cents on this, assuming you're not doing 1v1, or a smaller map, that's a completely different kettle of fish altogether:
STTC is not a game-winning aspect of VL. It usually helps when denying an enemy of a key planet (although you lose it too) or giving a quick boost to your economy to build a fast defense fleet. As KSSSWM said above me, it is far more effective to get trade and refineries to maximize profit.
Now, onto my advise.
First off: SCOUT. This applies to any strategy Scouting is very important for all factions, and for Vasari in particular because you can see neutral extractors this way. Your scouts can take those in case you didn't know. Fight for those. Vasari ships are expensive, and any additional income is always a plus. The enemy fighting for them too? Send supporting ships. I've seen huge fights break out over this before, and as hilarious as that is, it's sometimes worth it.
When your scouts are't grabbing up neutrals, have them on auto-explore and keep a steady stream of replacements/new scouts coming. What good is a massive fleet if you don't have the intelligence on your enemy to use it effectively? You don't want to jump into a minefield or a starbase unprepared, do you?
As VL (just Vasari in general actually), I usually focus on offensive expansion, most of the time.
You're usually quite a few jumps from an enemy on the maps you seem fond of, and have an ally around the same distance away. This gives you room to breathe, but you can't just relax. Be swift and aggressive with your expansions.
Start with building an Egg (Evacuator) as your starting capital ship, and a weapons lab to research Assailants. Most of the time, you don't need to invest in Skirmisher LFs, because they are usually considered a poor choice by most players. Now remember, you don't have to worry about fighting enemy players/AI right away, so you don't need a powerful starting cap. Plus, the Egg is considered the second best colony cap in terms of abilities and firepower, (TEC Akkan is the best economically) next to the Advent Mothership.
Split your forces, send your cap to a nearby asteroid or dwarf, and around 5 Assailants to another lightly defended planet of your choice, with a Migrator waiting to come in after the fight. Sometimes you get unlucky and have to make a few extra ships to accompany your cap to take deserts or terrans, but not always.
If you get screwed and have to research Ice/Volcanic colonization very early, build the imperial labs as well as the weapon lab at your home world and get going as fast as you can. This setback can cost you a lot of time if you're not careful.
Now, after heading out, clear the militia opposition in one of two ways:
Kill everything to maximize EXP for your cap ship.
Kill siege frigates/LRFs and make a couple turrets to kill the remaining militia, ad leave to continue your expansion. You can (and probably should) scuttle these for resources, or leave them to expand defense later.
After you get the first asteroid, build another weapons lab here, research corvettes, and add a few of them to your Assailant force. They help with drawing fire and killing siege/LRM frigates.
As you take planets and upgrade their infrastructure, add more ships as you see fit. Replace your losses too.
Taking these early allows for a good economy to fund a decent number of ships (Assailants mostly and possibly carriers later in this early game stage, diversifying my fleet more later) to take planets from enemies. Vasari can be a deadly force to reckon with early on if you do what you should.
After you build up as many planets as you can, you'll end up with a decent fleet of LRF and Corvettes. Now it is time to start actively scouting the enemy.
Chances are, a border has been created between you and your enemy. Build a few factories on this border planet to help with loss replacement and reinforcing your attacks. This allows for a much more swift response to spam of any kind. Usually around 20-30 corvettes can buy you enough time to make a better counter to anything, because they tend to counter popular spam decently, like fighters and LRFs.
When you're ready, pick your first target and send in a number of ships you think will be enough to take the planet. Don't send in everything, because enemies (human players in particular) usually assume that what you attack with is all you've got, but when you bring in more if you need to, it can cause them to flee. Keep more ships coming as you attack, 5 Assailants here, a few corvettes there, maybe a couple carriers if they have a lot of LRFs/strikecraft. Keep up the pressure, if they flee, send some ships after them while you clean up with your cap. Aggression is a powerful weapon. If you seem fearless, they're less likely to attack back.
I also like to build some siege frigates (a few cause they are pricey at take up a lot of fleet supply) to harass the enemy at undefended worlds. This is popular tactic used by the AI, and it's very effective against us humans. It causes us to have to allocate a few ships to stop the bombing, and in turn causes us to shift from focusing on anything else, like ship building, research, planet taking, etc. Works even better if you send a few supporting ships to help destroy structures and defend your bombing.
You can also send in some siege frigates with your attack forces, and use them to either assist with bombing or send them ahead with your ships after the enemy flees to really put the pressure on.
This is basically all you need to do to wipe out your nearest foe, and once you do that you can focus on helping allies if they need it, composing a fleet to counter the remaining enemies, fortifying choke points, building a better economy, the list goes on. You just need to get out of that early game to really do anything else. To survive is to adapt. Don't go into a game with any particular strategy set in stone. You can't win every game if you play the same each time, especially on randomly generated maps.