Make a post on one, see it on another

without users ever seeing the dashboard.

What level are these users? Authors? Contributers? Subscribers? All user levels have access to the dashboard, but not the same amount of access as an admin does. What is your end game here?

I am using NinjaForms to create posts.

NinjaForms is for creating forms. I have no idea how (or why) you are using it to create posts.

I would like the posts to show up on a different page

Do you mean that you want a page with a list of posts on it? If Date archives or Category archives or Tag archives won’t work for you, try a “post list” plugin.

All users will be contributors. I have used a NinjaForms addon, Frontend Editor.

I will make my intentions more clear as my question was poorly asked.

I am creating a free classifieds website and would like everything to be front end (never getting to see wordpress). I am having trouble creating a page to make a post, and sending that post to a specific category.

ex. user clicks post ad and is redirected to fill out a form. Category of automobile is selected and form data is filled out. Ad listing appears on the automobile section of the website.