Hello Dokfitz, and welcome to the forums.
The premier combo decks for Duelyst have been Songhai for a very long time (afaik) with it’s tendency towards bust damage. That being said, Songhai also plays very aggressively. Baconator (Tuskboar or another 2 drop + Mirror Meld + Attack Buffs) is an example of this. Other Songhai decks that may interest you include Spellhai, a deck that revolves around Spell synergies or Arcanysthai, a variant that includes cards such as Owlbeast Sage to buff minions.
Vanar and Lyonar also can pull combos using Owlbeast Sage by using Polarity and Divine Bond, turning the health buffs into attack power. These decks also use Spell synergy but are less synergistic compared to Songhai. Of the two (Lyonar vs Vanar) I’d recommend Vanar as Vanar has some of the best single-target removal spells in the game.
Another combo deck you may consider would be Artifact Vetruvian, a deck which has fallen out of favor. This deck revolves around using Aurora’s Tears or Time Maelstrom and artifacts to buff the general attack to over 25 points of damage. However this sort of combo is very fragile as it relies on artifacts and the general.
Final recommendation: Arcanyst (Owlpunch) Vanar. This deck is pretty budget in terms of crucial components (Owlbeast Sage, Polarity) in my opinion compared to some of the other decks mentioned above and still amusing to play.
WARNING: I have not tested this decklist and in fact have thrown it together as an example only. Use at your own risk.
At higher ranks I’d say currently Veteruvian (Zirix Midrange/Tempo), Songhai (Reva Aggro/Bacontor/Spellhai), and Vanar (Kara Zoo) are the most popular.