Post to a different page?

I am making a music blog with my friends. We want to have different pages for different genres on the top menu. Is it possible to make posts that will automatically go to these pages as well?

For example, we will have an “Indie” page. When we make a post on the main page we want to be able to choose the category as “Indie” and have it update the “Indie” page to also show this post. I know that we can have different “categories” and achieve something this way, but we want the genre to be clickable on the top menu. Maybe, perhaps, we could just put in some php on each of the pages and have it re-direct to the category page. I could not figure out how to implement php either. Every time I try to type in php, it just shows up as plain text. I have tried surrounding it with [code][/code] and [php][/php] but this does not seem to be the solution. Thanks ahead of time!