For me there are two Vasari fleets that I find very effective (n.b. this is excluding caps/Titans)
The first one is very strike craft based:
50% Transporter
30% Sentinel
20% Subverter
The Transporters would be decked out with bombers and the Subverter's phase bypass chance would buff the bombers, and also they could disable any flak the enemy had up. In this strategy you'll probably have to replace the Subverters quite often but it works a charm, especially against someone who's trying the same thing (knock out the flak and your bombers have free rein)
The other combo I use is more based around heavy hitters -
20% Enforcer
20% Skirmisher
20% Assailant
20% Overseer
20% Sentinel
With this fleet makeup I get the Enforcers to lead the charge with the Overseers keeping them alive, the Sentinels keeping strike craft at bay, the Assailants pounding away at long range and the Skirmishers running around for anti anti matter. This combo is quite effective against support caps and carrier caps, so I find.
Usually I use a combination of the two for all round pummeling power.
For caps I normally go with 4 Eggs, 4 Vulkoras, 4 Kortul, 2 Antorak and a Titan. The Eggs, Vulkoras and Kortul I use up on the front lines. Usually the Eggs are cap ship killers, the Kortuls I use against antimatter and the Vulkoras are for killing structures and LRM. The Antoraks, I find, are much more situational and much less useful in combat. Usually I don't really use them for much until they get to Level 6 and get their Phase Node ability. Then I run them through an enemy's planet (Distort Gravity and Phase Hull really nice for avoiding pursuit, also can use group of frigates as distraction) and get them behind enemy lines. Then they Phase Node and my fleet can completely bypass their defensive line and get to the roflstomping of their economy.