for me starting out by buying crystal from black market, upgrading the homeworld to lvl 4, buying the colony cap ship and taking colony lvl 1 ability is the way to go for all races against the AI. after that try to tech to something useful quickly, like LRMS & trade stations as TEC, assailants as vasari etc. get an asteroid asap and upgrade its people size but dont build anything except the mining buildings.

As a Vasari stop your scouts in any hostile free neutral no planet map that has extractors and cap them.

once you have 3 or 4 planets (possible to grab those rather quickly with the right research) running get the first fleet upgrade and build lots of lrm type ships.

the cpu is rather weak still and masses light frigate types which the lrm ones are strong against.
If you continue to expand aggressively you usually can bring the CPU is a defensive position and win easily from there on.

Another quick tip - don't worry about having fewer colonies than the AI. The AI is quick to overextend itself and ends up paying lots of resources to bring multiple colonies up to speed at once. In general, grabbing one or two asteroids and installing trade stations early on will give you an economy which is more productive than the AI, and for a lower cost in resources. This is especially true when colonizing Volcanic or Ice worlds - the cost to make them profitable is very high, not to mention the resources spent on the required techs.

see below link for more beginner information.

https://forums.sinsofasolarempire.com/?aid=301241