Tea, Coffee, Gold, Lapis, Citrus, and Salt are my favorite luxes as they give such nice yields and monopoly bonuses. If I'm going for a tradition game I love having a GA lux (i.e. Gold, Lapis, or Jade) as well as Marble and/or Stone in the capital, but any of the non-gold +10% luxes are also great for tradition play so I'm not super picky. Progress games are great for the mining/camp luxes as if you get a gold ruin, buy a worker, and go for the free worker policy first you can get an absurdly early monopoly and great capital yields in the right conditions. For Authority games I obviously love strategic-heavy starts as getting strat monopolies on Iron and Horses is just such a buff to aggressive play, beyond just having a practically unlimited ability to train Sword/Mounted units. The production-heavy luxes like Tea are also fantastic, and the tile-yield monopolies become so much stronger because you're working so many more of the tiles due to having more cities.
Hill starts are also just so much stronger than flatland starts in my experience. Even if I have a good luxury, if I'm playing a Tradition civ I'll restart a jungle start as I don't want to have to waste science on going to Bronze Working. I also don't like super hilly terrain if I'm going authority as I want to be able to move my units around quickly to war and tribute.
The ideal tradition start to me would probably be a floodplains start with a fair amount of wheat, single-tile ocean access and minimal ocean tiles in working range (for defense and GPTI maximization), Lapis as the main lux with Marble as the secondary, with a nearby stone and maybe a fish or two. Go Monument, Stonehenge, Shrine, Granary, then Mausoleum (if I can get the second policy quickly enough)
The ideal progress start to me would probably be on a hill next to a river in forest, Silver for the main lux and one of the camp luxes for the secondary, and lots of deer. Could be in plains forest or tundra forest, both offer good pantheon choices.
The ideal authority start to me would probably be on a hill (fresh water optional, as early wells are kinda great for authority IMO) in plains with scattered forest, Tea for the main lux and Ivory for the secondary, lots of horses and iron, and maybe a lake for an early growth tile.
There are definitely some insane terrain/pantheon combos that make just about any start good for any playstyle though (thinking Tundra forest with Stars and Sky, Purity with Sugar marshes and lakes, God of the Sea with Pearls monopoly).