show only the last post of each category and in a certain order

Hi everybody, I’m a newbie. I’ve tried to search in the forum before answering but I was not able to find what I’m looking for…

In few words: I’ve 2 categories in my blog – we suppose “up” and “bottom” – and I want show, in the home page, only the last post for each category. But I also want that the post in “up” category is always shown as first and the post in “bottom” category is always shown as second.

I’m trying to edit index.php in this way, but I think it’s an unnecessary work if someone else has done this yet.

Someone can help me, please? thanks in advance