Form for sender to automatically post online after approval from WP admin

Hello. I need help finding a form for the following situation:
I have an local chapter animal rights site that I’m relaunching in WP.

Owners who have lost their pet or need to find a new home for their pet will fill out a form (contact info, pet description, category (lost, found, searching for new home), upload up a few images, hit send and get sent to a confirmed page “Your announcement has been sent to the webmaster for approval, blah blah…” The owner will get an automatic confirmation mail once the announcement is online.

The WP admin approves the announcement and it gets published online in the correct category automatically…

I’m hoping this is possible, but I have NO idea how to search for this type of contact form. I ended up googling entire sentences which get me nowhere… Is this possible? If so, what is it called?

Any help would be great. Thanks.

PS. Since this is a non-profit animal rights org. website, everything needs to be free…