Even in a crowded niche is possible to go to the top. It is much harder, that's true. But not imposible. Your creativity, the way the content is organize (this is 50% of your success), providing a new, easier way to navigate (I'd give a good 40% of your success here), the design... everything will affect and drive you to success or failure. Small details in crowded niches matter even more.
I like anime too (it has not become popular in the last 5 years, it's been popular for ages, with its ups and downs) and, from time to time, I do visit anime sites. Most of these sites list the anime movies/series of their choice and their chapters. A few of them provide the ability to view these movies in HD, either free or by paying a small fee.
Others allow you to read the manga (with their own viewer, so you can't download the content)
A few are speciliazed in a particular series (like FullMetall Alchemist)
Another option to make money could be to link a store (with an affiliate program, of course) where the manga can be bought
Apart from doing what everybody else is doing, you should ask yourself what your web should have, something that you, as a fan, find that it's not anywhere else but that you would love to see. That new feature will probably put you at the top even if the niche is too full of competitors