Complex (To a beginner like me) Content Organization – Please Help!!

Before I go any further, my theme is the :TwentyTen theme and my website is https://www.allsportsnewsonline.com

Issue/Idea:
By the time I am finished with my blog, I will have a few hundred pages with the intent of most pages showing category or tag specific content.

For example, on my sports news blog, I only want my Dallas Cowboys Page to show posts assigned to the “Dallas Cowboys” category and my Cleveland Browns Page to show post assigned to the “Cleveland Browns” category.

A common fix is a widely used “List Category Posts” plugin. Unfortunately, this has created an issue with the styling I would like on my blog. It creates a very generic list with a bullet and a generic title and post display.

Example of style I do not wish to display: https://allsportsnewsonline.com/nfl/afc/afc-north/pittsburgh-steelers/

My ultimate objective is to show these posts on their respective pages as they would appear on my home page assuming that it is not static.

Example of desired post style: https://allsportsnewsonline.com/nfl/afc/afcn/clevelandbrowns/welcome-to-our-team-page-for-the-cleveland-browns/

I am a bit of a novice and I am willing to go about this any way as I am sure there are multiple ways to achieve what I aspire to accomplish.

Please excuse my terminology if I explained something incorrectly or didn’t state my objective clearly.

All help is appreciated!