Separating posts and pages

I am trying to make my search template more user friendly and am having trouble breaking out the posts and pages.

This is for my church website. You can see the search page I have now here:
https://www.churchthatcares.org/?s=ministry

Currently, I have my search results display as an unordered list. I would like to be able to do one of two things.

First choice would be to have two lists, one listing the posts that the search term falls in, the next listing the pages.

Second choice would be to have the individual list item to be displayed as

category: post title
Page: page title

I have tried that but adding the_category returns the default blog category for all of the pages.

HELP!!!