My two favourite civilisations are Poland, and Phoenicia.
I love Poland especially because they have so many different ways to excel, with different and sometimes mutually exclusive gameplay styles thanks to their diverse yet subtle toolkit. Their wildcard allows you extreme flexibility right from Code of Laws, and along with recent policy card changes they can make just about any government type work for whatever they need without ending up with too many red card slots, or not enough green card slots. Holy Sites gaining standard adjacency bonuses from districts is massive, meaning you can build tightly-packed cities surrounding Holy Sites while not worrying about Campus placement rivalry; if you take the River Goddess pantheon (in my opinion, the best for Poland) as well as optionally the Feed the World or Gurdwara beliefs, you escape the housing problem of tight city planning and can make viably tall cities as well to maximise gains from Theocracy. Common wisdom suggests that Reliquaries is their best main belief, but considering their ability to get high adjacency Holy Sites anywhere, I would argue that Work Ethic is just as good, if not better, especially if you are playing with less emphasis on religion or faith. Culture bombing with Encampments and forts can also create extremely cheeky ways to forward settle opponents, not to mention gaining absurd amounts of era score in the mid-game if you go to war - which is especially easy for Poland, because the Winged Hussar is one of the most powerful and tactical units in the game. Despite all of this, in part because of their high skill floor Poland is considered a fairly average civilisation, not especially strong, which makes me hope they will get more buffs. As long as those buffs do not take away from their diversity and flexibility, of course.
Phoenicia is fun for their unique, risky continent capital switcheroo. It requires that a lot of pieces come together, but is fantastic when it does. Phoenicia also has the most beautiful unique district in the game, one of the few which fully keeps its uniqueness throughout the game without succumbing to the genericisation of modern buildings - this is looking at you, Hansa. While they are nearly unbeatable on the sea thanks to their ridiculous healing ability (and despite their mediocre unique unit with an almost useless ability), they lose almost all of their bonuses if they have little access to water - but coastal cities have the consistent trouble of having few spots for district placement as well as lower base housing. This makes for a bad mix with Phoenicia's Government Plaza and district production bonuses, as in the early game you are extremely choked for district slots: you need a Cothon to make use of the sea and for fast settlers, but you also need a Campus for science to get the technologies to be able to actually embark on and use water tiles, but you want a Government Plaza for its bonuses and also the Ancestral Hall, and you might like an Entertainment Complex for the amenities, a Commercial Hub for even more gold, or especially some Theatre Squares to have a strong culture output to reach the great mid-game coastal/colonial policy cards and wonders... and so on. A lot of their abilities are out of sync and need to be fine-tuned, but the basis are good and very fun. Oh, and the free Writing eureka is flavourful but extremely silly: one of the easiest eurekas to get, unless you deliberately play an extreme archipelago map where you start on an isolated island, and even then that stacks the deck so hard against the AI that you might as well have won on game start by picking a naval civilisation on a water-heavy map. It could be changed into something much more interesting, in my opinion.