Good evening,
I am a very experienced API developer, I have developed my own API in the past using XML, however a REST API is easier to develop.
I do have some questions related to your requirements.
1) How to you intend to create & issue API keys to your users?
2) In what format do you need the database content delivered to your users? (CSV, XML, XLS etc)
3) Do you already have a database with the data you wish to send to your users, and does that data contain timestamps to identify when data was added? (for use with your criteria).
I can write this in PHP and it will work across any operating system so if you change server in the future it will continue to work.
I can develop this in my own environment where you can test the functionality, and once approved I can release all of the source code and documentation to you.
Should you have any questions or wish to review some of my prior work please let me know and I shall happily provide samples.
All the best,
Alec.