I would suggest you just do a conventional spam of TEC LRM spam, mixed with some flak. It doesn't take too long to get, its gives a ton of forward firepower, and is difficult to counter quickly. The LRM will knock down weaker SBs, kill his caps, and drive back any titans that you may have to face, The flak will keep corvettes and fighters at bay so your lrm don't get wiped out.
This strategy also allows you to build a big fleet quick, then eco so you can build more powerful ships like titans or orgevs to deal with higher level SBs. The only problem is if he SB rushes fast enough, you will not be able to counter.
If you must go Advent, you best bet is to carrier spam with corvette support. Do NOT build more than 2 carrier capital ships because they die too easy at lower levels. Focus on leveling up the two that you have. Remember that you only need about half the number of fighter squadrons to counter your opponents bombers. This should not be a problem as advent. This will force your opponent to build flak and LF, which are countered by illums and disciples.
Advent are not ideal for countering vasari though because their eco is weak. It takes forever to build enough ships to be effective. By that point, Huy may have STTC, which is a death sentence for an advent player. You best bet (depending on how far away your vasari opponent) may be to use the advents wonderful opening rush of LF and corvettes. Keep in mind though that this strategy is not very good against SBs. It will push your opponent back though so you can take more worlds though IF they do not successfully get a SB on one of your worlds.