Generally, a good starting fleet is a colony cap, with some scouts and LFs (For Vasari, their LRFs come early enough to be used instead). For the next ships, it really depends on what your enemy is making. Typically, most people go to LRFs early on in the game, so making more scouts and flak is highly recommended. Early on, most fleets are either scout/LF with LRFs coming in soon. With scout\LF fleets, going pure LF is the way to go.

With TEC, try to get Hoshiko cruisers quickly. They're very cheap and can make an enormous difference in an early battle. With Advent, getting Illuminators and Defense vessels are highly recommended. And Vasari... well, Assailants can come out extremely quickly, but otherwise, keep getting more of those and Sentinels until you can get out carriers.

Once HCs come out, you need Bombers and your own HCs. LRFs can work if you have enough, but are usually too frail to take on massed heavies. The exception is Advent; Illuminators can currently hold your own and even take out heavies. But generally, massed Bombers will kill them easily.

A little more info with vasari.

It depends on the size of the map. in small maps assailants with scouts and colony cap are good.

However in larger maps u may want to build more scouts so u can aquire a early neutral extractor advantage which is important for vasari. Vasari LR frigs are great but wont work unsupported cause besides the damage they do thanks to phase missles they relatively weak. so when u get them try to get a good ration of them and skimishers or scouts. When heavy cruisers are available? i would barely recommend even using vasasi HC's. Instead get more support craft and carriers. these are the areas where the vasari shine my eyes.

For advent(not my prefered race so forgive errors) Ilums are very powerful if ur comp stomping illums plus fighters are unbeatable. But advent especially u want balance in ship type.

In the end its as Darwin said build the counter to ur enemies ships jus be warned that not all those counters work as vasari especially those involving scouts light frigs or HC's

Yeah, the Vasari do have their problems. If the Overseer's jump degredations were cumulative, that would wreck game balance, but it would be awesome, because you could force an enemy fleet to go to sublight speeds between stars, and gain control over the entire phase network if you get them out quickly. But then again, if you had three, then thats 150% phase speed decrease, so how the hell would that work? I really like the Advent overall.