I am confused...
You want to build a website using PHP and host it up on a Linux system? If that is correct, then you have a few options:
By writing a page to just display the php info you can view the settings:
However, this doesn't allow for direct modification of the ini file. You would need to open the php.ini file and make the changes, and then save the file. You could do this over FTP or using SSH and a command line text editor such as pico, vim, nano or something similar.
Saving to the database doesn't make a whole lot of sense as the php.ini is a flat file, not a db type. I suppose you could set something up to read the php.ini as a string into a table, but that would be... strange. You could instead setup some sort of auto script (maybe using rsync) to download the php.ini at regular intervals to a local system for backup purposes.
And you shouldn't have to reboot the box after making changes, simply restarting the web server (apache probably) should suffice. How that is done depends on your distro, but may be something like: