Sins v 1.00
Okay, that's quite different than the current version of Sins. I hope someone else can corroborate what I'm telling you, because my experience here is limited.
There was a bug in that version that caused the illuminator to have capital-type damage, rather than anti-medium. As a result, Advent lacked a hard counter to light frigates, but could really smack around your capital ships with illuminators. Almost all TEC capital ships were bugged or underpowered in 1.00 anyways, so you if you're going TEC you probably don't need to bother bringing one to the fight.
TEC probably is your best pick, and there are three units in particular you should focus on: the Hoshiko, the Javelis LRM, and the Krosov Siege Frigate. In the original version of the game, the Krosov was cheaper, tougher, and more deadly than it is now. Combined with generally slow frigates and inferior strike craft capabilities in those days, they were regarded as obscenely overpowered. Use them to harass the enemy's flank. If your enemy tries the same thing on you, build a force of scouts to hunt them down. Scouts are one of the few units with the speed to chase down 1.00 siege frigates and are cheap enough that you can build a whole bunch cheaply.
For your military muscle, use the long range frigate, the Javelis LRM. This guy packs a ridiculously hard punch in 1.00. Combine with the hoshiko for mobile healing and you've got a tough and vicious pack of units to search and destroy the enemy. Avoid carriers, and eventually work towards heavies, and you should be in great shape.
Although it was before my time, my understanding was that in 1.00 Advent was considered a very weak faction. The opposite is true now.