Based on my very limited experience with this game, I can give you the lowdown on what I've learned about Vasari. Originally, they were my favorite race, so I understand the appeal of wanting to play them. Having said that, I switched to Advent because I felt like Advent is better than they are in almost every way, at least early game.
Please keep in mind that all these comments are made concerning multiplayer and competitive play, not against the AI which obviously it doesn't really matter which race you play, because you are facing a computer.
Vasari have a really rough start for reasons that have been discussed in this thread umpteen times and also that pretty much anyone would agree on. Their Light Frigs are underpowered, their Long-Range Frigs are inferior to the other races' (though you can get them quicker), their Scout is also inferior in the big picture. Their Capital Ships are nothing to marvel at, in my opinion Advent has the best ones because they synergize so well, even early on. Obviously Darvin disagrees with me about the capital ships, but he's a veteran, so his opinion probably counts for more there.
The only real early-game redeeming grace you find with Vasari are the fact that their Scouts can colonize asteroid field mines and that they can get a quick SB. I think the SB rush is more of a gimmick strategy than anything so in all actuality, you may have no real advantage over an opponent of a different race early game (unless the map is heavily covered in asteroid fields).
If you can hold out for the first 25 minutes or so though, things may start to change for your favor. The Vasari economy tree is the best in my opinion, with such beautiful things as easy population increases for several types of planets, crystal+metal upgrades together, 15% credit reductions for anything you buy, fast planet populating to get those new planets gushing out the cash, and of course early refineries if you are in a good spot. If you can take advantage of even a couple of these economic bonuses early on, it can put you in a huge advantage over your opponent. In a 1v1 this is extremely hard in my opinion (because of the tendency for rush), but it can more easily be done in 2v2, and certainly 3v3 etc.
Once you've made it to mid-game with a decent economy and upgrades, you can start to shine. Your long-range frigates, though inferior early on, can become quite superior with phase missile upgrades and in conjuction with Subverters. I have been told that your strike craft (fighters and bombers) are the toughest and most powerful in the game, and since they all use missiles, also become greatly improved with the phase missile upgrade.
The loved and feared Phase Stabilizers are one of the most prominent and memorable features about Vasari, and its what sets them apart from the other races in terms of mobility and map control.
To make a long story short: Early game you're always going to have it rough, late game, if you do it correctly, you can dominate.
Hopefully they buff some things next patch to make them a little more useful early game, I think most people would agree they need it.
In Single Player it's pretty much just what Darvin said. Unlock your Assailants ASAP, they you can be pretty aggressive because the computer isn't going to build mass scouts to counter you. You can proceed to bully them around, taking their meteors and smaller planets early, then late game you just overwhelm them with your larger force.
Sorry if I made any mistakes or misleading comments, like I said I'm new at this too.
Wing