Arkham City was for a long while considered the best, but age has arguably been kinder to Asylum (thanks to storytelling) and Knight (thanks to streamlining/modernization).
I don’t think there is any question on how to answer the literal post, though. If you could only get one of them, it’s Asylum.
Also, I would not recommend binging these games unless you are REALLY feeling it when you finish Asylum. The chief complaint about them was always that they did not change the formula around enough between games. I have to think playing them back to back exacerbates that.
All the usual problems you expect with lists like these.