Man, that's a tough one because 'best' is so subjective, but the real trick is finding shows where the fan service feels earned by the plot, not just slapped on. A lot of ecchi harem can feel like a checklist of tropes, but the ones that stick with me usually have a solid hook beyond the girls.
For a genuinely compelling storyline, I'd have to point to 'High School DxD'. I know, I know, it's the obvious answer, but there's a reason. The world-building around the Three Factions and the Sacred Gears creates actual stakes. Issei's growth from a pervy underdog to someone with real power and responsibility gives the harem elements a foundation. The fanservice is blatant, but the plot about exorcists, fallen angels, and a looming war has a surprising amount of weight.
On the other end of the spectrum, 'Monster Musume' is a different beast, pun intended. The story is basically slice-of-life, but the compelling part is the world-building and the social commentary wrapped in absurd comedy. The 'Interspecies Cultural Exchange' act and the sheer logistical nightmare of dating a lamia or a harpie create a unique narrative tension that's more about coexistence than saving the world. It's goofy, but the character dynamics feel genuine amidst the chaos.
A slightly older pick that doesn't get enough love is 'Rosario + Vampire'. The manga is infinitely better, but even the anime's first season has a core 'fish out of water' story with Tsukune trying to survive in a school for monsters while hiding his humanity. The plot gets overshadowed by filler later on, but the initial premise of danger and secrecy provides a backbone the pure fluff shows lack. The fan service is there, but the threat of being discovered or eaten adds a layer the later seasons sadly abandoned.