My strategy for advent is simple. The only ship worth having is the halcyon. Build one, or two. I prefer one, as a higher level halcyon early on is a very strong advantage, and it minimizes the micro you have to do to keep it alive. Since I began this strategy I have only had my halcyon sniped once in a year due to an early LRM spam. You then use the rest of your cash to spam disciples and defense vessels, along with some illuminators. You have to plan for an illuminator buildup, as you need some time to build up 30+ (the golden number for illums). While you are building up you need to prevent any illuminator losses, since killing illums really helps your enemy since they still are worth a crapload of experience. To do so you need to be on the attack, or pretending to be. Make them chase your fleet if you can, prevent losses and waste their time. always have scouts with your fleet so you don't wind up in a horrible trap!
Upgrade the disciple and defense vessel attack, and presto you have a mean fleet. Since advent ships are so expensive and you have very few economic options in the early game, you need to focus more on building your fleet up. If you are playing multiplayer online you have to focus all of your energy on fleet to have a shot. Advent are the most assailable race, and when you begin attacking an enemy you should already be researching repair platforms because most of the time you will have to retreat your halcyon because it doesn't last long in a fight.
People like to say "shields are SOOOOO good", but in all reality the guardian+progen+shield upgrade combo is an advent endgame strategy that isn't going to be effective in an early multiplayer game, as it is way too expensive, and gives you little to no offensive capability. What good is a defense that eventually crumbles and you can't strike back?
Advent suffer from a focus fire issue. With the right ships they can defend against focus firing effectively. But at all times they lack the ability to build up a strong focus fire to kill capital ships and starbases with their ships. The only way to build capital/starbase killing power early is to spam carriers with bombers. A halcyon with full fighters and the anti fighter ability will take care of enemy fighters/bombers, and you will have the advantage. This strategy is easily countered with a pure LF spam by the enemy, so keep them scouted at all times! If you see a LF spam you need to go LRM if you can, or spam your own LF's and choose a battle location closer to your home so that you will have the resupply advantage.
You can try advent mines, but they are costly and they take forever to activate so they are nearly worthless. Also, they don't do much damage and tend to all home in on one target and therefore aren't much of a threat to an enemy fleet.