There's no better way to start a series by catching the viewer's attention and also establishing what to expect in terms of artstyle, plot, and what's unique about it. I think Durarara!! does that perfectly. The first 6 or 7 episodes have this unique feel to them, like every episode is an indivual art piece from intro to outro. I could honestly only watch one a day with how "meaty" the episodes are xD everything from the worldbuilding to the characters to the soundtrack make Durarara!! something truly special, and the way everything's introduced makes it even better.

Another example of this is the anime called K, otherwise known as K-Project. PLEASEPLEASEPLEASE, I BEG OF YOU. GO WATCH THE FIRST TWO EPISODES AT THE LEAST. Beware the heavy fanservice, which I admit is a drag. It doesn't remove from the experience too heavily, at least in my opinion, because the plot, artstyle and world are all too interesting for me to care about fanservice rofl

K is extremely unique. There's nothing like it, but Durarara's got something similar. Go watch it!!