Hi there,
Sounds pretty straightforward to me. Happy to build a fully custom app for you.
I imagine we would have sort of timeline for lost things. When listing a found thing people will be able to easily pick the location on map where they have found it and/or where the thing is at the moment. They would be able to attach photos and if they found someone ID with it, they would be able to specify the ID number too.
There would be categories which you could manage through the admin section.
People who have lost their things could search and browse through categories of found things. Additionally, if they can't find it, they will be able to create a "seek" for their lost thing, and they will get an email notification once the thing matches the specified keywords or persons ID number.
I would implement ad management for you so you can easily change ads without editing any code.
It would have a responsive, clean and simple design. Code would be clean, commented and unencrypted. I would code in PHP+MySQL (CodeIgniter framework), Bootstrap, JS, etc...
Let me know if you have any questions. Eager to hear more about the project and work with you.
Regards,
Julijan