Something simple and seasonal would be idea. One of the hallmarks of anime is it's seasonal nature. Many series are short-lived. But every season fans look forward to a new menu of anime programs, sometimes for the better or for the worse. A static layout that accents the seasons and changes by the season would be nice.
Each season could outline a popular genre of anime and manga. The badges could be something that fit the season -- like a leaf for fall, droplet for spring, snowflake for winter, and a sun for summer.
One of the biggest challenges with making a banner about anime is being able to capture the essence of the subculture without using and specific IPs. Sure we can loosely imply parodies though commissions, the results will likely skew towards popular mainstream tastes. The anime and manga industry is the way it is through the diversity of talents of the content and tastes creators.
While I initially proposed a os-tan style mascot/idol type poster character, I such a meme would be of any help to promote. This SE site. Character design guidelines, branding guidelines take too much time and effort. A simple picturesque seasonal vector landscape shot with the silhouette of a few more well known characters in the background might suffice.
Maybe it can be a bench at a trains station or storefront with anime and manga in the background (on a bill board or station sign billboard) a tree to on each side, or in the background. Make be something like a cross between:
But not with as much detail.
One single location, as the seasons pass. The only real color palette, might be the primary/secondary color for a season plus the badge icons.
Nothing too tall or wide. Naturally with not as much detail. Shorter and narrower to keep up with the standard banner sizes.
The overall look and feel can be simple caricatures or veil/full silhouettes like these:
Simple and flat looking, with layers like the above.
In general, something low-key yet recognizable by fans like this background:
Subtle, simple, yet picturesque.
If the concept of changing seasons is too complicated, then it's probably best to pick the ONE season you like best (I would summer or winter) and run with that.
The meta site can be just the line art of the main site to accent a conceptual nature motif or something, like a behind the scenes making of banner.