Well, it depends on your personal preferences. If you are a fan of chaotic engagements and spectacular visual effects, then Warhammer is the best option, where you can deploy giants, mammoths, kamikaze goblins and dinosaurs riding... dinosaurs. If you like something more relaxed, basically a long series of battles briefly interrupted with meaningless campaign breaks, then you should choose everything from Empire to Attila. Keep in mind that Rome II still suffers from a variety of bugs, but Empire, even if you adore the period, is
practically unplayable, unless you install a mod. Last but not least, Medieval II and Rome I are not only by far the most moddable games, but are also very feature-rich, in what concerns immersive mechanics. For example, the late-game challenge is provided by the "distance-to-capital" mechanic, which forbids irrational expansion, due to low public order and lack of profitability. Granted, it's not as cartoon-fun as suddenly everyone declaring war against you for no apparent reason in Shogun or the Huns indefinitely spamming hordes, until you kill their king thrice or more. In my opinion, the older games are much more satisfying, from a more realistic trait-system and more coherent family tree to more atmospheric UI and cleverly integrated logistics, but I recognize the fact that, for example, the lack of auto-replenishment, albeit objectively more immersive, can pose difficulties to excited video-game players.