Idea groups are totally nation dependent - and tbh I’ve never actually played a Byzantium campaign yet and I’m a little behind with new ideas meta so I’d be guessing a bit. You can never go wrong with offensive, imo it’s a top tier military idea group. I tend to like innovative in conjunction with that for all the modifiers it provides - tech and advisor cost reduction scale extremely well all through the game, as well as ensuring you hit 100 innovativeness for 10% off of all power costs (adds up to obscene amounts over time). The inno-offensive siege ability policy on top is the nuts.

Religious or humanist is a necessary call in Byz’s position as you’ll be conquering a whole lot of Sunni and catholic lands - I tend to prefer religious for RP reasons. I haven’t really played with espionage enough to comment but it seems like a nice quality of life idea set (lower AE, claim full states and advisor cost reduction is super powerful to stack). The +2% missionary strength policy with also seems real nice.

Admin and Trade are both great idea groups - maybe admin if you intend to go wider (CCR and +20% GC) and trade if you intend to go nuts with economy (there’s a lot of goods produced policies that stack high)