Well there are three main issues new players to Sins tend to fall into that limits their ability to progress against harder AIs. These are...
1. Expand too slow
2. Research too much, too fast
3. build too many capitalships
(1) Now I know you said you're an offensive player, so hopefully this is less of a deal to you. However you might be missing some of the tools of the trade. Most decent to good players will expand with at least two different forces. They'll either build a colony/carrier capitalship (with colony frigate) and go attack planets, preferably in the direction of a choke point or less defended volcanic and higher planets. A favorite pro trick is to just destroy the turrets, colonize, then build a turret ASAP then send your cap to the next planet. Any remaining militia will be destroyed by the turret.
They'll also build a colony frigate with corvettes or in the Vasari's case assailants and begin taking asteroids/dwarfs and less defended volcanics/ice planets. After getting basic colonization techs start focusing on maxing out your initial fleet supply, which should be sufficient for all but the most heavily fortified terrans/deserts.
(2) Now there are some techs you'll need to get ASAP. New frigate designs (especially corvettes, LRF and flak), planet colonization techs, etc. But the stat boosting techs don't really become noticeable until you have a decent sized fleet. The tier 0 upgrades are okay if you have some extra cash to throw around, and the terran planet upgrades can be a good investment most times so long as you don't get rushed. But when you only have 20 frigates a tier 2 extra laser damage upgrade isn't going to be a huge deal. You should wait until you have say 100, then it can certainly be felt.
(3) Too many capitalships. Caps are great for their abilities, but per cost and fleet supply they have worse stats than frigates. Some caps like carriers do become competitive once they reach high levels, but until then they tend to hold back your fleets firepower, which can cause you to loose early/mid engagements against a player who build 50 fleet supply of corvettes or LRFs. Also remember all capitalships in a gravity well share XP with each other and titans. This means they'll all grow at a slower rate, and since a few high level caps (and certainly a high level titan) are better than many weak ones, you don't want too many capitalships in the same fleet. That said once a cap/titan reaches level 10 it will no longer take any XP, so after this you can start adding more caps if you want to.
Also the Vasari Rebels are considered to be fairly OP right now. If you're having trouble mid game, consider rushing right to the phase jumping starbase tech ASAP. It need 8 military labs but the AI really struggles at taking out starbases, especially a fully upgraded "Orkulus Rex".