Since you say you're a veteran RTS player and asking about build orders I assume you don't need the very basics. That said, to be even decent at Sins it just takes a lot of experimenting with all the techs and units, since the tutorials are minimal and there is no campaign to easy you through it. This map might be of help if you'd rather do that without any hostile AI trying to kill you.

Anyways for build order. Most of the time your starting capitalship will be either your race's colony cap or carrier cap (that would be the Jarassul Evacuator AKA space egg, or the Skirantra Carrier for Vasari Loyalists). You should probably build one of each lab on your homeworld, and research Assailants ASAP. Cue up a Skirmisher or two and a colony frigate (2 if going for the Skirantra) and possibly more scouts depending on the map. Send your pair skirmishers to an asteroid an moon as soon as they are built, and keep the colony ship on the edge of the gravity well. Destroy the siege frigate first, then bring in the colony ship and take it. Do roughly the same thing for the capitalship, but it can take out all but heavily defended desert and terran worlds if needed. Reinforce either with assailants as you start making them.

After that its basically try to expand as fast as possible, preferably in the direction of key choke points. Unlike Starcraft all the real estate in Sins is based on planets, so getting as many planets as possible early is both great for early game economics as well as setting up late game trade and research potential.

Some miscellaneous faction tips.

*In competitive play many Vasari players will try to build a starbase on the enemy's home world. Its a risk if its spotted in time, but if you get a colony ship in undetected and successfully build one it can be a crippling blow. This is made possible that the Vasari build starbases with colony ships, which you can build straight away, are cheaper than starbase constructors, and only need two labs to deploy.

*Currently most Vasari loyalists try to go for Striped to the Core ASAP. With skilled management of your economy its certainly possible to get 7 civic labs in under a half hour. From there, the raw amount of income gained from striping can fuel a huge fleet build up and even a titan fairly quickly, reinforced by striping newly conquered enemy planets. You should never go completely mobile though, you can spawn in more reinforcements from phase stabalizers build from your titan, but you can't chose exactly what ships you get, so some shipbuilding facilities are highly recommended.

*Phase missiles and phase stabalizers are awesome Vasari tech advantages that should be exploited as much as possible.

*The VL titan might seem somewhat lackluster early on, but once it reaches level 6 it can quite literally eat tons of enemy ships for breakfast.

Thanks for the fantastic responses guys, I've been applying your information and its been going quite well. I still have some more simplistic questions however: 

I'm figuring out how to level my capital ship faster--it's leveling but i'm getting outleveled on the one capital ship I do have (i got the space egg first for colonization efficiency)

Another small issue is figuring out how the scout extractor building ability works. I gather i can use it to make extractors on asteroids but I've not had it work successfully yet? 

just small interface stuff! Thanks for the help so far!

On planets you can colonize you just build them like any other structure. Some planets that aren't colonizeable also have resource asteroids though, and come with "neutral extractors" already built. If they exist on say a gas giant or ionic storm, just send your colony frigate in and it will eventually auto use the ability and capture them.

Well for the most part you just get levels for blowing stuff up. When a ship dies, every enemy capitalship and titan gets its XP value / number of objects getting the experience. This is quite important, as its one of the main reasons to try not to build too many capitalships in one fleet, as they will "cannibalize" each others XP thanks to XP sharing. Its generally better to have a few high level caps than many low level ones (Vasari loyalists have economic reasons to build capitalships so they are an exception, but you should try not to have too many in active combat), and certainly a high level titan.

As for getting it to level up faster, as Vasari you really can only purchase capitalship training. This allows you to spend credits to get your cap ships up to level 3 (or 4 with research), but this is generally a bad idea early game since that's when you need those credits for lots of other things (a few rush strategies use it though). The TEC Loyalists and Advent do have some techs that can help with experience gain rate. Other than that, just kill more stuff with your capitalships is all you can do.

As for corvettes, I build a lot of them to expand early on as Advent and TEC, but since the Vasari Corvettes are tier 2 I tend to avoid them, since I can get Assailants easier and I like to max out my starting fleet ASAP. I haven't played a lot of competitive Vasari lately though since a lot of other players do, so I might be wrong on this.

The scout ability doesn't work on Asteroids, it's for neutral extractors in asteroid belts, space junks, etc. (there are several kinds of systems that have extractors but no planet).

My usual build order with Vasari is...

1. Immediately queue the following: Evacuator, 3 Scouts, 2 LFs. Send out scouts to start exploring.

This may be more scouts than most people build, but I think the ability to capture neutral extractors is the single biggest advantage the Vasari have. This is an absolutely insane boost to your economy in the early game. Therefore I want to find neutral extractors as quickly as possible and claim them. If it turns out you have extra scouts you can use them to help clear up pirates or keep tabs on your enemies.

2. As soon as Evacuator finishes, send it towards an adjacent asteroid or dwarf. Use the information from your scouting to expand in the most efficient possible way. Scuttle the Capital Ship Factory for extra resources.

3. If there are asteroids/dwarfs in multiple directions, I queue a Colony Frigate and 2 more LFs and send them in the opposite direction of my Cap. (At this point I have a lone Cap expanding in one direction and a Colony Frig supported by 4 LFs going the other way. You want to try to send the Cap towards the more heavily defended planets as it can take far more punishment than the Colony Frig, as well as benefitting from experience.) If there's only one direction I want to expand, I skip the Colony Frig and just build 2 more LFs to help with expansion.

4. Now my plans start to vary according to the situation... If I have access to lots of asteroids and dwarfs, and/or a nearby opponent I want to rush, I'll build 2 Military Labs on my homeworld. This opens up corvettes, lrfs, and sentinels, which can be used as necessary to counter the enemy fleet, as well as ship upgrades. It also allows starbase construction, which you can use to plant an aggressive starbase (against an opponent who has neglected fleet production, bild a starbase at their homeworld or other crucial planet).

If I have lots of Ice/Volcanic planets I want to colonize and/or no nearby opponents, I'll go for a more "econ" approach by building 2 Civic Labs and research Ice or Volcanic occupation and maybe the Terran population upgrade while focusing on expansion.